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Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra.
A generalization of Quillen’s lemma and its application to the Weyl algebras
A. Joseph · 1977
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The diamond lemma for ring theory
G. Bergman · 1978
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An analogue of the Sklyanin algebra
M. Odesskii · 1986
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Distance-Regular Graphs
A. E. Brouwer, A. M. Cohen, and A. Neumaier · 1989
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Twisted second quantization
W. Pusz and S. L. Woronowicz · 1989
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Quantum deformations of SU(2)
D. B. Fairlie · 1990
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A class of algebras similar to the enveloping algebra of s l ( 2 ) sl(2)
S. P. Smith · 1990
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The incidence algebra of a uniform poset
P. Terwilliger · 1990
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Gauge theories, vertex models, and quantum groups
E. Witten · 1990
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Quantization of Chern-Simons gauge theory with complex gauge group
E. Witten · 1991
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R R -matrix formulation of deformed boson algebra
J. Van der Jeugt · 1993
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Conformal 𝔰 𝔩 2 \mathfrak{sl}_{2} enveloping algebras
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Lectures on quantum groups
J. C. Jantzen · 1996
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Quantum matroids
P. Terwilliger · 1996
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Down-up algebras
G. Benkart and T. Roby · 1998
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Representations of the cyclically symmetric q q -deformed algebra so q ( 3 ) {\rm so}_{q}(3)
M. Havlíček, A. U. Klimyk, and S. Pošta · 1999
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Isomorphism problems and groups of automorphisms for generalized Weyl algebras
V. Bavula and D. A. Jordan · 2001
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Homogenized down-up algebras
T. Cassidy · 2003
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Simple modules of the Witten-Woronowicz algebra
V. Bavula and F. van Oystaeyen · 2004
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Basic properties of generalized down-up algebras
T. Cassidy and B. Shelton · 2004
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On the centre of two-parameter quantum groups
G. Benkart, S. Kang, and K. Lee · 2006
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An SU ( 2 ) {\rm SU}(2) analogue of the Azbel-Hofstadter Hamiltonian
E. G. Floratos and S. Nicolis · 1998
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An extended q q -deformed su ( 2 ) {\rm su}(2) algebra and the Bloch electron problem
K. Fujikawa and H. Kubo · 1998
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Representation theory and q q -boson realizations of Witten’s su ( 2 ) {\rm su}(2) and su ( 1 , 1 ) {\rm su}(1,1) deformations
C. Delbecq and C. Quesne
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Bipartite Q Q -polynomial distance-regular graphs and uniform posets
S. Miklavic and P. Terwilliger
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On representations of quantum groups U q ( f m ( K , H ) ) Uq(fm(K,H))
X. Tang and Y. Xu · 2008
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C. Worawannotai · 2012
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