Braided doubles and rational Cherednik algebrasCitation formats

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Braided doubles and rational Cherednik algebras. / Bazlov, Yuri; Berenstein, Arkady.

In: Advances in Mathematics, Vol. 220, No. 5, 20.03.2009, p. 1466-1530.

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Harvard

Bazlov, Y & Berenstein, A 2009, 'Braided doubles and rational Cherednik algebras', Advances in Mathematics, vol. 220, no. 5, pp. 1466-1530. https://doi.org/10.1016/j.aim.2008.11.004

APA

Bazlov, Y., & Berenstein, A. (2009). Braided doubles and rational Cherednik algebras. Advances in Mathematics, 220(5), 1466-1530. https://doi.org/10.1016/j.aim.2008.11.004

Vancouver

Bazlov Y, Berenstein A. Braided doubles and rational Cherednik algebras. Advances in Mathematics. 2009 Mar 20;220(5):1466-1530. https://doi.org/10.1016/j.aim.2008.11.004

Author

Bazlov, Yuri ; Berenstein, Arkady. / Braided doubles and rational Cherednik algebras. In: Advances in Mathematics. 2009 ; Vol. 220, No. 5. pp. 1466-1530.

Bibtex

@article{e0a9b309cd3745759f1ea06ee632985a,
title = "Braided doubles and rational Cherednik algebras",
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. {\textcopyright} 2008 Elsevier Inc. All rights reserved.",
keywords = "Braided double, Cherednik algebra, Dunkl operator, Nichols algebra",
author = "Yuri Bazlov and Arkady Berenstein",
note = "Open access now via Elsevier",
year = "2009",
month = mar,
day = "20",
doi = "10.1016/j.aim.2008.11.004",
language = "English",
volume = "220",
pages = "1466--1530",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Elsevier BV",
number = "5",

}

RIS

TY - JOUR

T1 - Braided doubles and rational Cherednik algebras

AU - Bazlov, Yuri

AU - Berenstein, Arkady

N1 - Open access now via Elsevier

PY - 2009/3/20

Y1 - 2009/3/20

N2 - 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.

AB - 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.

KW - Braided double

KW - Cherednik algebra

KW - Dunkl operator

KW - Nichols algebra

U2 - 10.1016/j.aim.2008.11.004

DO - 10.1016/j.aim.2008.11.004

M3 - Article

VL - 220

SP - 1466

EP - 1530

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 5

ER -