Poisson double extensions
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A double Ore extension was introduced by Zhang and Zhang (2008) to study a class of Artin-Shelter regular algebras. Here we give a definition of Poisson double extension which may be considered as an analogue of double Ore extension, and show that algebras in a class of double Ore extensions are deformation quantizations of Poisson double extensions. We also investigate the modular derivations of Poisson double extensions and the relationship between Poisson double extensions and iterated Poisson polynomial extensions. Results are illustrated by examples.
KeywordsPoisson double extension semiclassical limit deformation quantization
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The first author was supported by National Natural Science Foundation of China (Grant No. 11331006). The second author was supported by National Research Foundation of Korea (Grant No. NRF-2017R1A2B4008388), and he thanks the Korea Institute for Advanced Study for the warm hospitality during the preparation of this paper. The third author was supported by National Natural Science Foundation of China (Grant Nos. 11301180 and 11771085). All the authors thank the referees for their helpful suggestions and comments.
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