Braided doubles and rational Cherednik algebras

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Abstract

We introduce and study a large class of algebras with triangular decomposition which we call braided doubles. Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. We classify braided doubles in terms of quasi-Yetter-Drinfeld (QYD) modules over Hopf algebras which turn out to be a generalisation of the ordinary Yetter-Drinfeld modules. To each braiding (a solution to the braid equation) we associate a QYD-module and the corresponding braided Heisenberg double-this is a quantum deformation of the Weyl algebra where the role of polynomial algebras is played by Nichols-Woronowicz algebras. Our main result is that any rational Cherednik algebra canonically embeds in the braided Heisenberg double attached to the corresponding complex reflection group. © 2008 Elsevier Inc. All rights reserved.

Bibliographical metadata

Original languageEnglish
Pages (from-to)1466-1530
Number of pages64
JournalAdvances in Mathematics
Volume220
Issue number5
DOIs
Publication statusPublished - 20 Mar 2009