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Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors.
The trace of totally positive and real algebraic integers
Carl Ludwig Siegel · 1945
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Über Sequenzen ganzer Zahlen, von denen keine zu n n teilerfremd ist. I, II, III
Ernst Jacobsthal · 1961
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Über eine zahlentheoretische Funktion von Jacobsthal
Hans-Joachim Kanold · 1967
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Sums of three roots of unity
A. J. Jones · 1968
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On a conjecture of R. M. Robinson about sums of roots of unity
J. W. S. Cassels · 1969
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Some properties of the spectrum of a graph
John H. Smith · 1970
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On the error term in the linear sieve
H. Iwaniec · 1971
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On the maximum modulus of cyclotomic integers
J. H. Loxton · 1972
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Trigonometric Diophantine equations (On vanishing sums of roots of unity)
J. H. Conway and A. J. Jones · 1976
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Index for subfactors
Vaughan F. R. Jones · 1983
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The mean values of totally real algebraic integers
C. J. Smyth · 1984
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Principal graphs of subfactors in the index range 4 < [ M : N ] < 3 + 2 4<[M:N]<3+\sqrt{2}
Uffe Haagerup · 1994
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Conformal field theory
Philippe Di Francesco, Pierre Mathieu, and David Sénéchal · 1997
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Principal graphs of subfactors with small Jones index
Dietmar Bisch · 1998
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The number of intersection points made by the diagonals of a regular polygon
Bjorn Poonen and Michael Rubinstein · 1998
Cited alongside, same era.
Tensor categories with fusion rules of self-duality for finite abelian groups
Daisuke Tambara and Shigeru Yamagami · 1998
Cited alongside, same era.
Exotic subfactors of finite depth with Jones indices ( 5 + 13 ) / 2 (5+\sqrt{13})/2 and ( 5 + 17 ) / 2 (5+\sqrt{17})/2
Marta Asaeda and Uffe Haagerup · 1999
On fusion categories
Pavel Etingof, Dmitri Nikshych, and Viktor Ostrik · 2005
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Salem numbers, Pisot numbers, Mahler measure, and graphs
James McKee and Chris Smyth · 2005
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Galois groups and an obstruction to principal graphs of subfactors
Marta Asaeda · 2007
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Group-theoretical properties of nilpotent modular categories, 2007
Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik · 2007
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Weakly group-theoretical and solvable fusion categories, 2008
Pavel Etingof, Dmitri Nikshych, and Victor Ostrik · 2008
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On Haagerup’s list of potential principal graphs of subfactors
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Cited alongside, same era.
Lectures on tensor categories and modular functors
Bojko Bakalov and Alexander Kirillov, Jr · 2001
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Algebraic graph theory
Chris Godsil and Gordon Royle · 2001
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The structure of sectors associated with Longo-Rehren inclusions. II. Examples
Masaki Izumi · 2001
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Unpublished notes, 2001
Feng Xu · 2001
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On a q q -analogue of the McKay correspondence and the ADE classification of 𝔰 𝔩 2 \mathfrak{sl}_{2} conformal field theories
Alexander Kirillov, Jr. and Viktor Ostrik · 2002
Cited alongside, same era.
Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten
L. Kronecker
Cited in the paper.
Marta Asaeda and Seidai Yasuda · 2009
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Constructing the extended haagerup planar algebra, 2009
Stephen Bigelow, Scott Morrison, Emily Peters, and Noah Snyder · 2009
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On braided fusion categories i, 2009
Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik · 2009
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Cyclotomic factors of Coxeter polynomials
Benedict H. Gross, Eriko Hironaka, and Curtis T. McMullen · 2009
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On formal codegrees of fusion categories
Victor Ostrik · 2009
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