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2016 Finite dimensional Hopf actions on algebraic quantizations
Pavel Etingof, Chelsea Walton
Algebra Number Theory 10(10): 2287-2310 (2016). DOI: 10.2140/ant.2016.10.2287

Abstract

Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra, we showed that a semisimple Hopf action on a Weyl algebra over a polynomial algebra k[z1,,zs] factors through a group action, and this in fact holds for any finite dimensional Hopf action if s = 0. We also generalized these results to finite dimensional Hopf actions on algebras of differential operators. In this work we establish similar results for Hopf actions on other algebraic quantizations of commutative domains. This includes universal enveloping algebras of finite dimensional Lie algebras, spherical symplectic reflection algebras, quantum Hamiltonian reductions of Weyl algebras (in particular, quantized quiver varieties), finite W-algebras and their central reductions, quantum polynomial algebras, twisted homogeneous coordinate rings of abelian varieties, and Sklyanin algebras. The generalization in the last three cases uses a result from algebraic number theory due to A. Perucca.

Citation

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Pavel Etingof. Chelsea Walton. "Finite dimensional Hopf actions on algebraic quantizations." Algebra Number Theory 10 (10) 2287 - 2310, 2016. https://doi.org/10.2140/ant.2016.10.2287

Information

Received: 19 May 2016; Revised: 1 August 2016; Accepted: 22 October 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1355.16030
MathSciNet: MR3582020
Digital Object Identifier: 10.2140/ant.2016.10.2287

Subjects:
Primary: 16T05
Secondary: 13A35, 16S38, 16S80

Rights: Copyright © 2016 Mathematical Sciences Publishers

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