發(fā)布時間：2018-10-09 07:44

【摘要】：Heisenberg-Virasoro代數(shù)是一類重要的無限維李代數(shù),它的表示理論在數(shù)學(xué)和物理里有著重要的應(yīng)用.本文主要研究了 Heisenberg-Virasoro代數(shù)的結(jié)構(gòu)與表示方面的若干問題.文章前半部分在前人工作基礎(chǔ)上進一步考察了 Heisenberg-Virasoro代數(shù)上正部作用局部有限的模的結(jié)構(gòu),并對一種特殊情形給出了比較清楚的刻畫.文章后半部分主要研究了Heisenberg-Virasoro代數(shù)上的Rota-Baxter算子的結(jié)構(gòu),并對權(quán)為0的齊次Rota-Baxter算子給出了刻畫.
[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.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O152.5

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本文編號：2258534