Cherednik, Hecke and quantum algebras as free Frobenius and Calabi–Yau extensions

Brown, K.A., Gordon, I.G. and Stroppel, C. (2008) Cherednik, Hecke and quantum algebras as free Frobenius and Calabi–Yau extensions. Journal of Algebra, 319(3), pp. 1007-1034. (doi: 10.1016/j.jalgebra.2007.10.026)

Abstract

We show how the existence of a PBW-basis and a large enough central subalgebra can be used to deduce that an algebra is Frobenius. We apply this to rational Cherednik algebras, Hecke algebras, quantised universal enveloping algebras, quantum Borels and quantised function algebras. In particular, we give a positive answer to [R. Rouquier, Representations of rational Cherednik algebras, in: Infinite-Dimensional Aspects of Representation Theory and Applications, Amer. Math. Soc., 2005, pp. 103–131] stating that the restricted rational Cherednik algebra at the value t=0 is symmetric.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stroppel, Dr Catharina and Brown, Professor Ken
• Authors: Brown, K.A., Gordon, I.G., and Stroppel, C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Algebra
• ISSN: 0021-8693
• ISSN (Online): 1090-266X
• Published Online: 26 November 2007