Poisson double extensions

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 701-720
• 页数: 20页
• 语种: 英文

摘要

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 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.