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

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

2006-07-06

arxiv.org/abs/math/0607170v1

Journal of Algebra 2008

Mathematics

Representation Theory

Scientific paper

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. This is done by considering the examples of rational Cherednik algebras, Hecke algebras, quantised universal enveloping algebras, quantum Borels and quantised function algebras. In particular, we give a positive answer to \cite[Problem 6]{Rouquier} stating that the restricted rational Cherednik algebra at the value $t=0$ is symmetric.

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