关于Heisenberg-Virasoro代数的结构与表示的若干问题
发布时间：2018-10-09 07:44
【摘要】：Heisenberg-Virasoro代数是一类重要的无限维李代数,它的表示理论在数学和物理里有着重要的应用.本文主要研究了 Heisenberg-Virasoro代数的结构与表示方面的若干问题.文章前半部分在前人工作基础上进一步考察了 Heisenberg-Virasoro代数上正部作用局部有限的模的结构,并对一种特殊情形给出了比较清楚的刻画.文章后半部分主要研究了Heisenberg-Virasoro代数上的Rota-Baxter算子的结构,并对权为0的齐次Rota-Baxter算子给出了刻画.
[Abstract]:Heisenberg-Virasoro algebra is an important infinite dimensional lie algebra. Its representation theory has important applications in mathematics and physics. In this paper, we study the structure and representation of Heisenberg-Virasoro algebras. In the first half of this paper, the structure of locally finite modules of positive action on Heisenberg-Virasoro algebras is further investigated on the basis of previous work, and a relatively clear characterization of a special case is given. In the second half of this paper, the structure of Rota-Baxter operators on Heisenberg-Virasoro algebras is studied, and the characterization of homogeneous Rota-Baxter operators with weight 0 is given.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5
本文编号：2258534
[Abstract]:Heisenberg-Virasoro algebra is an important infinite dimensional lie algebra. Its representation theory has important applications in mathematics and physics. In this paper, we study the structure and representation of Heisenberg-Virasoro algebras. In the first half of this paper, the structure of locally finite modules of positive action on Heisenberg-Virasoro algebras is further investigated on the basis of previous work, and a relatively clear characterization of a special case is given. In the second half of this paper, the structure of Rota-Baxter operators on Heisenberg-Virasoro algebras is studied, and the characterization of homogeneous Rota-Baxter operators with weight 0 is given.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5
【参考文献】
相关期刊论文 前3条
1 陈海波;申冉;张建刚;;广义Heisenberg-Virasoro代数的量子化[J];数学学报;2014年01期
2 程永胜;张明亮;;Heisenberg-Virasoro代数的q-形变的量子群结构[J];纯粹数学与应用数学;2009年04期
3 ;Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra[J];Acta Mathematica Sinica(English Series);2007年01期
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