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Braided doubles and rational Cherednik algebras
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Bazlov, Yuri and Berenstein, Arkady (2009) Braided doubles and rational Cherednik algebras. Advances in Mathematics, Vol.220 (No.5). pp. 1466-1530. doi:10.1016/j.aim.2008.11.004 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2008.11.004
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) modides 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. (C) 2008 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Advances in Mathematics | ||||
| Publisher: | Academic Press | ||||
| ISSN: | 0001-8708 | ||||
| Official Date: | 20 March 2009 | ||||
| Dates: |
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| Volume: | Vol.220 | ||||
| Number: | No.5 | ||||
| Number of Pages: | 65 | ||||
| Page Range: | pp. 1466-1530 | ||||
| DOI: | 10.1016/j.aim.2008.11.004 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF) | ||||
| Grant number: | GR/SI0629/01 (EPSRC), EP/D065801/1 (EPSRC), DMS-0501103 (NSF) |
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