Poisson double extensions  

作　　者：Qi Lou Sei-Qwon Oh Shengqiang Wang 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China [2]Department of Mathematics,Chungnam National University,Daejeon 34134,Republic of Korea [3]Department of Mathematics,East China University of Science and Technology,Shanghai 200237,China

出　　处：《Science China Mathematics》2020年第4期701-720,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11331006);supported by National Natural Science Foundation of China(Grant Nos.11301180 and 11771085);supported by National Research Foundation of Korea(Grant No.NRF2017R1A2B4008388)。

摘　　要：A double Ore extension was introduced by Zhang and Zhang(2008)to study a class of ArtinShelter regular algebras.Here we give a definition of Poisson double extension which may be considered as an analogue of the 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.A double Ore extension was introduced by Zhang and Zhang(2008) to study a class of ArtinShelter regular algebras. Here we give a definition of Poisson double extension which may be considered as an analogue of the 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.

关 键 词：POISSON DOUBLE extension SEMICLASSICAL LIMIT deformation QUANTIZATION 

分 类 号：O15[理学—数学]