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Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language of category theory.
Invertible phases of matter with spatial symmetry
Daniel S. Freed and Michael J. Hopkins · 1901
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Defect Verlinde formula for edge excitations in topological order
Ce Shen and Ling-Yan Hung · 1901
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Galois conjugated tensor fusion categories and nonunitary conformal field theory
Laurens Lootens, Robijn Vanhove, Jutho Haegeman, and Frank Verstraete · 1902
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A factorization homology primer
David Ayala and John Francis · 1903
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Topological phase transition on the edge of two-dimensional ℤ 2 \mathbb{Z}_{2} topological order
Wei-Qiang Chen, Chao-Ming Jian, Liang Kong, Yi-Zhuang You, and Hao Zheng · 1903
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Tube algebras, excitations statistics and compactification in gauge models of topological phases
Alex Bullivant and Clement Delcamp · 1905
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Condensations in higher categories
Davide Gaiotto and Theo Johnson-Freyd · 1905
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The center of monoidal 2-categories in 3+1d Dijkgraaf-Witten theory
Liang Kong, Yin Tian, and Shan Zhou · 1905
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A mathematical theory of gapless edges of 2d topological orders. Part I
Liang Kong and Hao Zheng · 1905
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Choreographed entanglement dances: Topological states of quantum matter
Xiao-Gang Wen · 1906
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Zur theorie der matrices
Oskar Perron · 1907
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String-net models for nonspherical pivotal fusion categories
Ingo Runkel · 1907
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Minimal modular extensions for super-Tannakian categories
César F. Venegas-Ramírez · 1908
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Excitations in strict 2-group higher gauge models of topological phases
Alex Bullivant and Clement Delcamp · 1909
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Extension theory for braided-enriched fusion categories
Corey Jones, Scott Morrison, David Penneys, and Julia Plavnik · 1910
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Microscopic definitions of anyon data
Kyle Kawagoe and Michael Levin · 1910
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Wenjie Xi, Zhi-Hao Zhang, Zheng-Cheng Gu, and Wei-Qiang Chen · 1911
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Ueber matrizen aus nicht negativen elementen
Georg Frobenius · 1912
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Pointed Drinfeld center functor
Liang Kong, Wei Yuan, and Hao Zheng · 1912
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A mathematical theory of gapless edges of 2d topological orders. Part II
Liang Kong and Hao Zheng · 1912
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Über den dualitätssatz der nichtkommutativen topologischen gruppen
Tadao Tannaka · 1939
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A principle of duality for bicompact groups and quadratic block algebras
Mark Grigorievich Krein · 1949
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The unreasonable effectiveness of mathematics in the natural sciences
Eugene P. Wigner · 1960
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Local stabilizer codes in three dimensions without string logical operators
Jeongwan Haah · 1962
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Catégories avec multiplication
Jean Bénabou · 1963
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Natural associativity and commutativity
Saunders MacLane · 1963
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Quadratic forms on finite groups, and related topics
C.T.C. Wall · 1963
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Catégories relatives
Jean Bénabou · 1965
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Symmetric Bilinear Forms
John Milnor and Dale Husemoller · 1973
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A Course in Arithmetic
Jean-Pierre Serre · 1973
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Surgery with coefficients
R. James Milgram · 1974
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Categories for the Working Mathematician
Saunders MacLane · 1978
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Tannakian categories
P. Deligne and J. S. Milne · 1982
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Two-dimensional magnetotransport in the extreme quantum limit
D. C. Tsui, H. L. Stormer, and A. C. Gossard · 1982
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Quantum mechanics of fractional-spin particles
Frank Wilczek · 1982
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Remarks on the Laughlin theory of the fractionally quantized Hall effect
P. W. Anderson · 1983
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Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations
R. B. Laughlin · 1983
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Fractional statistics and the quantum Hall effect
Daniel Arovas, J. R. Schrieffer, and Frank Wilczek · 1984
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Statistics of quasiparticles and the hierarchy of fractional quantized hall states
B. I. Halperin · 1984
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Gauge invariance and fractional quantum Hall effect
R. Tao and Yong-Shi Wu · 1984
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General theory for quantum statistics in two dimensions
Yong-Shi Wu · 1984
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Quantized Hall conductance as a topological invariant
Qian Niu, D. J. Thouless, and Yong-Shi Wu · 1985
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Long-range order and the fractional quantum Hall effect
D. J. Thouless · 1985
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Quantum Physics
James Glimm and Arthur Jaffe · 1987
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Equivalence of the resonating-valence-bond and fractional quantum Hall states
V. Kalmeyer and R. B. Laughlin · 1987
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Rationality in conformal field theory
Greg Anderson and Greg Moore · 1988
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Topological quantum field theories
Michael Atiyah · 1988
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The definition of conformal field theory
G. Segal · 1988
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Toward classification of conformal theories
Cumrun Vafa · 1988
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Fusion rules and modular transformations in 2D conformal field theory
Erik Verlinde · 1988
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Superselection sectors with braid group statistics and exchange algebras
K. Fredenhagen, K. H. Rehren, and B. Schroer · 1989
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Classical and quantum conformal field theory
Gregory Moore and Nathan Seiberg · 1989
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Vacuum degeneracy of chiral spin states in compactified space
Xiao-Gang Wen · 1989
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Quantum field theory and the Jones polynomial
Edward Witten · 1989
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Chiral spin states and superconductivity
Xiao-Gang Wen, Frank Wilczek, and A. Zee · 1989
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Effective-field-theory model for the fractional quantum Hall effect
S. C. Zhang, T. H. Hansson, and S. Kivelson · 1989
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Effective theories of the fractional quantum Hall effect at generic filling fractions
B. Blok and X. G. Wen · 1990
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Effective theories of the fractional quantum Hall effect: Hierarchy construction
B. Blok and X. G. Wen · 1990
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Topological gauge theories and group cohomology
Robbert Dijkgraaf and Edward Witten · 1990
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Braid statistics in local quantum theory
J. Fröhlich and F. Gabbiani · 1990
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Lectures on RCFT
Gregory Moore and Nathan Seiberg · 1990
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Excitation structure of the hierarchy scheme in the fractional quantum hall effect
N. Read · 1990
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Braid group statistics and their superselection rules
Karl-Henning Rehren · 1990
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Topological orders in rigid states
Xiao-Gang Wen · 1990
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Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
Xiao-Gang Wen and Qian Niu · 1990
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Structure of the microscopic theory of the hierarchical fractional quantum hall effect
B. Blok and X. G. Wen · 1991
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Tortile Yang-Baxter operators in tensor categories
André Joyal and Ross Street · 1991
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Representations, duals and quantum doubles of monoidal categories
Shahn Majid · 1991
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Invariants of 3-manifolds via link polynomials and quantum groups
N. Reshetikhin and V. G. Turaev · 1991
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Non-Abelian statistics in the fractional quantum Hall states
Xiao-Gang Wen · 1991
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Fractional quantum Hall effect and nonabelian statistics
N. Read and G. Moore · 1992
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Quantum Hall Effect
Michael Stone · 1992
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State sum invariants of 3-manifolds and quantum 6j-symbols
V.G. Turaev and O.Y. Viro · 1992
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Classification of Abelian quantum Hall states and matrix formulation of topological fluids
X. G. Wen and A. Zee · 1992
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Framed tangles and a theorem of Deligne on braided deformations of Tannakian categories
David N. Yetter · 1992
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Braided tensor categories
A. Joyal and R. Street · 1993
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Dimensional reduction in quantum gravity
G. ’t Hooft · 1993
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Lattice topological field theory in two dimensions
M. Fukuma, S. Hosono, and H. Kawai · 1994
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Tensor products of modules for a vertex operator algebra and vertex tensor categories
Yi-Zhi Huang and James Lepowsky · 1994
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Homological algebra of mirror symmetry
Maxim Kontsevich · 1994
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A theory of tensor products for modulé categories for a vertex operator algebra, IV
Yi-Zhi Huang · 1995
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Quantum groups
Christian Kassel · 1995
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Invariants of piecewise-linear 3-manifolds
John W. Barrett and Bruce W. Westbury · 1996
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Local Quantum Physics
Rudolf Haag · 1996
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Quantized thermal transport in the fractional quantum hall effect
C. L. Kane and Matthew P. A. Fisher · 1997
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A theory of dimension
Roberto Longo and John E. Roberts · 1997
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Semisimple and modular categories from link invariants
Vladimir Turaev and Hans Wenzl · 1997
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Quantum codes on a lattice with boundary
S. B. Bravyi and A. Yu. Kitaev · 1998
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On α \alpha -induction, chiral generators and modular invariants for subfactors
Jens Böckenhauer, David E. Evans, and Yasuyuki Kawahigashi · 1999
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Spherical categories
John W Barrett and Bruce W Westbury · 1999
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The large N limit of superconformal field theories and supergravity
Juan Maldacena · 1999
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Group categories and their field theories
Frank Quinn · 1999
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Chiral structure of modular invariants for subfactors
Jens Böckenhauer, David E. Evans, and Yasuyuki Kawahigashi · 2000
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Catégories prémodulaires, modularisations et invariants des variétés de dimension 3
Alain Bruguières · 2000
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Galois theory for braided tensor categories and the modular closure
Michael Müger · 2000
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Homotopy field theory in dimension 3 and crossed group-categories
Vladimir Turaev · 2000
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Modular categories of types B, C and D
A. Beliakova and Ch. Blanchet · 2001
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Longo-Rehren subfactors arising from α \alpha -induction
Jens Böckenhauer, David E. Evans, and Yasuyuki Kawahigashi · 2001
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Lectures on tensor categories and modular functors
Bojko Bakalov and Alexander Kirillov, Jr · 2001
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Quantum computation and the localization of modular functors
Michael H. Freedman · 2001
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Modular categories and orbifold models II
Alexander Kirillov, Jr · 2001
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A duality for modules over monoidal categories of representations of semisimple Hopf algebras
D Tambara · 2001
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Broken quantum symmetry and confinement phases in planar physics
F. A. Bais, B. J. Schroers, and J. K. Slingerland · 2002
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Thermal transport in chiral conformal theories and hierarchical quantum hall states
Andrea Cappelli, Marina Huerta, and Guillermo R. Zemba · 2002
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Catégories tensorielles
P. Deligne · 2002
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A modular functor which is universal for quantum computation
Michael H. Freedman, Michael Larsen, and Zhenghan Wang · 2002
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On a q q -analogue of the McKay correspondence and the ADE classification of 𝔰 𝔩 ^ 2 \hat{\mathfrak{sl}}_{2} conformal field theories
Alexander Kirillov, Jr. and Viktor Ostrik · 2002
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Mirror anomaly in fermionic topological orders
Bin-Bin Mao and Chenjie Wang · 2002
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Invertible braided tensor categories
Adrien Brochier, David Jordan, Pavel Safronov, and Noah Snyder · 2003
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Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
Alexander F Bais, Bernd J Schroers, and Joost K Slingerland · 2003
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On the classification of topological orders
Theo Johnson-Freyd · 2003
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Fault-tolerant quantum computation by anyons
Alexei Kitaev · 2003
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Classification of topological phases with finite internal symmetries in all dimensions
Liang Kong, Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang, and Hao Zheng · 2003
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From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories
Michael Müger · 2003
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From subfactors to categories and topology II: The quantum double of tensor categories and subfactors
Michael Müger · 2003
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On the structure of modular categories
Michael Müger · 2003
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Module categories, weak Hopf algebras and modular invariants
Victor Ostrik · 2003
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Module categories over the Drinfeld double of a finite group
Viktor Ostrik · 2003
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Framed discs operads and Batalin-Vilkovisky algebras
Paolo Salvatore and Nathalie Wahl · 2003
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Quantum order from string-net condensations and the origin of light and massless fermions
Xiao-Gang Wen · 2003
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Chiral algebras
Alexander Beilinson and Vladimir Drinfeld · 2004
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On tensor categories attached to cells in affine Weyl groups
R. Bezrukavnikov · 2004
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Homotopy-theoretic approach to SPT phases in action: ℤ 16 \mathbb{Z}_{16} classication of three-dimensional superconductors
Kitaev · 2015
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Fermionic symmetry protected topological phases and cobordisms
Anton Kapustin, Ryan Thorngren, Alex Turzillo, and Zitao Wang · 2015
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Liang Kong, Xiao-Gang Wen, and Hao Zheng · 2015
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Gapped domain walls, gapped boundaries, and topological degeneracy
Tian Lan, Juven C. Wang, and Xiao-Gang Wen · 2015
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An analogue of Radford’s S 4 S^{4} formula for finite tensor categories
Pavel Etingof, Dmitri Nikshych, and Viktor Ostrik · 2004
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Finite tensor categories
P. Etingof and V. Ostrik · 2004
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Generalized string-net model for unitary fusion categories without tetrahedral symmetry
Alexander Hahn and Ramona Wolf · 2004
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Galois extensions of braided tensor categories and braided crossed G G -categories
Michael Müger · 2004
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Frobenius duality in C ∗ {C}^{*} -tensor categories
Shigeru Yamagami · 2004
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Quantum glassiness in strongly correlated clean systems: An example of topological overprotection
Claudio Chamon · 2005
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Juven C. Wang and Xiao-Gang Wen · 2015
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Twisted gauge theory model of topological phases in three dimensions
Yidun Wan, Juven C. Wang, and Huan He · 2015
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Interacting topological insulator and emergent grand unified theory
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Bei Zeng and Xiao-Gang Wen · 2015
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Origin of fermion masses without spontaneous symmetry breaking
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Factorization homology of stratified spaces
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