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Finite dimensional Hopf actions on algebraic quantizations

Author(s)
Etingof, Pavel I; Walton, Chelsea
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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[z 1 ,… z s ] 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.
Date issued
2016-12
URI
http://hdl.handle.net/1721.1/115879
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Algebra & Number Theory
Publisher
Mathematical Sciences Publishers
Citation
Etingof, Pavel and Chelsea Walton. “Finite Dimensional Hopf Actions on Algebraic Quantizations.” Algebra & Number Theory 10, 10 (December 2016): 2287–2310 © 2016 Mathematical Sciences Publishers
Version: Author's final manuscript
ISSN
1944-7833
1937-0652

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