Algebr Represent Theor https://doi.org/10.1007/s10468-018-9787-3 Truncated Quantum Drinfeld Hecke Algebras and Hochschild Cohomology 1 2 Lauren Grimley · Christine Uhl Received: 8 November 2017 / Accepted: 19 April 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke algebras. We give the necessary and sufficient conditions for which these algebras occur, using Bergman’s Diamond Lemma. We compute the relevant Hochschild cohomology to make explicit the connection between Hochschild cohomology and truncated quantum Drinfeld Hecke alge- bras. To demonstrate the variance of the allowed algebras, we compute both classical type examples and demonstrate an example that does not arise as a factor algebra of a quantum Drinfeld Hecke algebra. Keywords Hochschild cohomology · Poincare-Birkhoff-W ´ itt deformations · Skew group algebra Mathematics Subject Classification (2010) 16S35 · 16S80 · 16E40 1 Introduction The class of Drinfeld Hecke algebras occur naturally as deformations of the skew group algebra S(V ) G, the (semi-direct product) algebra formed by a finite group G acting Presented
Algebras and Representation Theory – Springer Journals
Published: May 31, 2018
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