Poisson double extensions

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 def...

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Bibliographic Details
Published in:Science China. Mathematics 2020-04, Vol.63 (4), p.701-720
Main Authors: Lou, Qi, Oh, Sei-Qwon, Wang, Shengqiang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Polynomials
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-017-9333-x