Lectures on Algebraic Quantum Groups

By Kenneth A. Brown, K. Goodearl. 2002

545 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c6f0ee132ec5aaab35e4bb56c7d9b52597a80c14

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Citations in the corpus

Quantum cluster algebras (2004, background): “(Unfortunately, the Poisson bracket used in [16] and borrowed from[17] is the opposite of the one in[3].”
Braided symmetric and exterior algebras (2005, methodology): “We start with the definition of the quantized enveloping algebra associated with a complex reductive Lie algebra g (our standard reference here will be [10]).”
Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras (2006, methodology): “Recall, from [ BG2 , I.2.2-I.2.4] for example, that Oq(SLn) is generated by elements Xij for i, j = 1, . . . , n, with relations as given there.”
The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras (2010, methodology): “We refer the reader to Brown and Goodearl [6] and the references therein for generalizations of the Gelfand–Kirillov conjecture for quantized enveloping algebras.”
Prime regular Hopf algebras of GK‐dimension one (2008, background): “A ) belong to the same clique of maxspecA (in the sense of [ BG2 , I.16.2], for example).”
Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings (2008, background): “Let B be the localization C[D −1 q ], where Dq is the quantum determinant x11x22 − q −1 x12x21 (which is a central element in C). Then B is a Hopf algebra denoted by Oq(GL2) [ BG , Definition I.1.10].”
Centers of degenerate cyclotomic Hecke algebras and parabolic category (2006, background): “However, Iain Gordon has pointed out that this already follows directly by a general result of M¨uller [ BG , III.9.2], since Hd is finite as a module over its center.”
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation (2016, background): “In the context of quantum groups and Hopf algebras such solutions are often referred to as R-matrices (see for example [7, 27]).”