Poisson代数的平凡扩张的模导子  

Modular derivation of the trivial extension of Poisson algebras

作　　者：朱灿[1] 梁嘉威 李耀飞 ZHU Can;LIANG Jiawei;LI Yaofei(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2020年第5期436-440,共5页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11771085,11871125);上海市科委科研计划项目(19ZR1434600)。

摘　　要：设A是Poisson代数,M是A上的左Poisson模,则在A通过M的平凡扩张代数A■M上存在Poisson结构。当M取成A本身或其线性对偶A*时,则平凡扩张代数A■A*和A■A都是Frobenius Poisson代数。计算了这两类Frobenius Poisson代数的模导子,这个结果可视作有限维代数的平凡扩张的Nakayama自同构在Poisson代数中对应的结论。Let A be a Poisson algebra,M be a left Poisson module over A.Then,there is a Poisson algebra structure on the trivial extension algebra A■M of by M.Assuming that M is A itself or the linear dual A*of A,then both A■A*and A■A are Frobenius Poisson algebras.The modular derivation for these two classes of the trivial extension of Poisson algebras was calculated.These results can be viewed as the corresponding conclusions on the Nakayama automorphism of the trivial extension of finite dimensional algebras.

关 键 词：POISSON代数 平凡扩张 模导子 

分 类 号：O151.21[理学—数学]