Hochschild cohomology and quantum Drinfeld Hecke algebras Academic Article

abstract

• 2016, Springer International Publishing. Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups, and we exploit computations from Naidu et al. (Proc Am Math Soc 139:15531567, 2011) for diagonal actions. By combining our work with recent results of Levandovskyy and Shepler (Can J Math 66:874901, 2014) we produce examples of quantum Drinfeld Hecke algebras. These algebras generalize the braided Cherednik algebras of Bazlov and Berenstein (Selecta Math 14(34):325372,2009).

authors

• Witherspoon, Sarah

published proceedings

• Selecta Mathematica

author list (cited authors)

• Naidu, D., & Witherspoon, S.

citation count

• 4

complete list of authors

• Naidu, Deepak||Witherspoon, Sarah

publication date

• July 2016

publisher

• Springer Nature  Publisher

published in

• Selecta Mathematica  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00029-016-0224-3

start page

• 1537

end page

• 1561

volume

• 22

issue

• 3

URL

• http://dx.doi.org/10.1007/s00029-016-0224-3