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Finite dimensional Hopf actions on deformation quantizations


Authors: Pavel Etingof and Chelsea Walton
Journal: Proc. Amer. Math. Soc. 145 (2017), 1917-1925
MSC (2010): Primary 16T05, 16S80, 17B63, 16W70
DOI: https://doi.org/10.1090/proc/13356
Published electronically: October 27, 2016
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Abstract: We study when a finite dimensional Hopf action on a quantum formal deformation $ A$ of a commutative domain $ A_0$ (i.e., a deformation quantization) must factor through a group algebra. In particular, we show that this occurs when the Poisson center of the fraction field of $ A_0$ is trivial.


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Additional Information

Pavel Etingof
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: etingof@math.mit.edu

Chelsea Walton
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: notlaw@temple.edu

DOI: https://doi.org/10.1090/proc/13356
Keywords: Deformation quantization, filtered deformation, Hopf algebra action, Poisson center
Received by editor(s): February 21, 2016
Received by editor(s) in revised form: July 2, 2016
Published electronically: October 27, 2016
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society