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Universal enveloping algebras of Poisson Ore extensions


Authors: Jiafeng Lü, Xingting Wang and Guangbin Zhuang
Journal: Proc. Amer. Math. Soc. 143 (2015), 4633-4645
MSC (2010): Primary 17B63, 17B35, 16S10
DOI: https://doi.org/10.1090/S0002-9939-2015-12631-7
Published electronically: March 31, 2015
MathSciNet review: 3391023
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Abstract: We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As a consequence, we observe certain ring-theoretic invariants of the universal enveloping algebras that are preserved under iterated Poisson-Ore extensions. We apply our results to iterated quadratic Poisson algebras arising from semiclassical limits of quantized coordinate rings and a family of graded Poisson algebras of Poisson structures of rank at most two.


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Additional Information

Jiafeng Lü
Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People’s Republic of China
Email: jiafenglv@gmail.com

Xingting Wang
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Address at time of publication: Department of Mathematics, University of California, San Diego, CA 92093
Email: xiw199@ucsd.edu

Guangbin Zhuang
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email: gzhuang@usc.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12631-7
Keywords: Poisson algebra, universal enveloping algebra, Ore extension
Received by editor(s): April 4, 2014
Received by editor(s) in revised form: July 30, 2014
Published electronically: March 31, 2015
Additional Notes: The first author was supported by the National Natural Science Foundation of China (No. 11001245, 11271335 and 11101288)
The second author was partially supported by the U. S. National Science Foundation [DMS0855743]
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society