超Virasoro代数的一类单模及其实现-基础数学专业毕业论文.docx

黑龙江大学硕士学位论文
中文摘要
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本文首先介绍了李代数、李超代数和Virasoro代数的国内外发展现状和趋势以及本文研究的目的和意义.
然后介绍了超Virasoro代数的定义和相关基础知识,取超Virasoro代数的子代数的诱导模,通过证明诱导模的子模与其本身相等来证明超Virasoro代数一类模的单性.
最后通过证明一些新的单模与文中构造的这一类超Virasoro单模同构,将其实现,并且给出例子.
关键词:Virasoro代数,诱导模,局部有限,局部幂零.
万方数据
Abstract
Virasoro algebra and its superalgebra which has important applications in mathematics and physics and many other articles have studied the structure of order Virasoro algebra and its recent years the re— search on this topic is also more active.
In this paper,we study the development status,trend and significance of Lie
algebras,lie superalgebra and Virasoro algebras
Then introduces the definition of super-Virasoro algebras and related basic knowledge,induce modulo algebra over super-Virasoro algebra,by proving the sub- module induced module with its own equal,to prove that the simple of suDer. Virasoro algebra.
Finally,by the proof of some new simple module isomorphism with super—
Virasoro simple module,put it into realization,and gives examples. Keywords:Virasoro algebra;induced module;locally nilpotent;locally finite.
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万方数据
黑龙江大学硕士学位论文
目录中文摘要.....,.............................. I Abstract,.................................... II
目录.......................................III 符号说明,..........,........................IV 第1章绪论................................... 1
.....。.......。............... 1
...................,.. 1
............................ 3
第2章预备知识................................. 4
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第3章超Virasoro模的单性...................,....... 8
....................... 8
..........................,......10 第4章超Virasoro单模的实现.........................12 。..。。....。.。。。。。。。。。...。.12
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