一类形变Lie代数的结构与表示  

Structures and representations of a family of deformed Lie algebras

作　　者：陈洪佳 郜云 徐大树 赵琦 Hongjia Chen;Yun Gao;Dashu Xu;Qi Zhao

机构地区：[1]中国科学技术大学数学科学学院,合肥230026 [2]Department of Mathematics and Statistics,York University,Toronto M3J 1P3,Canada

出　　处：《中国科学:数学》2025年第1期3-14,共12页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:11931009,12101152,12161141001和12171132);中央高校基本科研业务费专项资金资助项目。

摘　　要：扭Heisenberg-Virasoro代数是复数域上一类重要的无限维Lie代数,它与一类曲线的模空间有关.本文对无中心扭Heisenberg-Virasoro代数的一族形变Lie代数G_(β)的结构与表示展开研究.主要结果包括:(1)确定不同G_(β)之间的同构关系;(2)刻画G_(β)的导子Lie代数与泛中心扩张;(3)分类G_(β)的U(CL_(0))秩1自由模,并给出这些模不可约的充分必要条件.在可约的情形下,本文确定了其唯一非零真子模.The twisted Heisenberg-Virasoro algebra is an important infinite-dimensional Lie algebra,closely related to moduli spaces of certain curves.In this paper,we delve into the structures and representations of a family of deformed Lie algebras,denoted by G_(β),associated with the untwisted Heisenberg-Virasoro algebra.The main results include:we determine the isomorphism relations among G_(β)’s;we compute the Lie algebra of derivations and the universal central extension of G_(β);and we classify the rank 1 free U(CL_(0))-modules of G_(β)and provide necessary and sufficient conditions for their irreducibility.In the case of reducibility,we determine the unique nonzero proper submodule.

关 键 词：扭Heisenberg-Virasoro代数 导子Lie代数 泛中心扩张 不可约模 秩1自由模 

分 类 号：O152.5[理学—数学]