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Generalized Weyl Algebras (GWAs) are defined by Bavula and Hodges. Their representation theory resembles those of Lie algebras, and they found extensive use in noncommutative resolutions of Kleinian singularities. The class is known to contain the ordinary Weyl algebras, the enveloping algebra U(sl_2) and its quantum deformation U_q(sl_2). In this talk, after a brief survey of GWAs and their twisted analogues, I will show that many rank-1 quantum groups, and Podleś spheres are all examples of GWAs. Time permitting, I will also talk about their Hochschild homology.

Link to the Seminar is :

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603130546547?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d