Universal enveloping algebras of Poisson Ore extensions
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- by Jiafeng Lü, Xingting Wang and Guangbin Zhuang PDF
- Proc. Amer. Math. Soc. 143 (2015), 4633-4645 Request permission
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.References
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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
- MR Author ID: 1029882
- Email: xiw199@ucsd.edu
- Guangbin Zhuang
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
- Email: gzhuang@usc.edu
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3391023