Virasoro-like代数及其q相似上的模

发布时间：2018-04-25 09:37

  本文选题：Witt代数 + Virasoro-like代数　； 参考：《郑州大学》2016年硕士论文

【摘要】：设d是正整数.d维洛朗多项式环Ad=C[t1±1,t2±1…,td±1]是交换结合代数,称它的导子李代数为Witt代数,记作Wd.量子环面代数Cq是类似于Ad的非交换结合代数,它的导子李代数我们记为Der(Cq)当d=2时,Witt代数W2有自然子代数L=L2以及去掉Cartan子代数后的L=L2,我们统称为Virasoro-like代数；此时称Der(Cq)的自然子代数G(q)＝L2(q),L(q)＝L2(q)为q-Virasoro-like代数.1986年,沈光宇在Wd上定义了一类权模：设a∈Cd, b∈C,V是g[d模,且单位矩阵在其上的作用是常数b,令Fbα(V)= V(?)d,则Fbα(V)成为一个自然的Wd模.函子Fbα也称为Larsson函子,后来Rao刻画了这类权模的结构.当d=2时,Fbα(V)可以看作Virasoro-like代数上的模,类似地,我们也可以定义q-Virasoro-like代数上的模Fqα(V).本文中,我们用统一的方法研究了这些模的不可约性,主要结果有：(1)我们确定了Fbα(V)的不可约性.特别地,当权空间V是无限维时,我们得到Virasoro-like代数上一类新的权空间无限维的不可约模；(2)无论V是有限还是无限维不可约s[2模,模Fqα(V)都可以分解成一个不可约子模与另一个子模的直和,同时我们也确定了另一个子模的不可约性.此外,我们还刻画了代数L上C[(?)1,(?)2]-作用自由的模的结构,它同构于Q(Λ2,α).
[Abstract]:Let d be a positive integer.D dimensional Laurent polynomial ring Ad=C[t1 + 1, T2 + 1... TD + 1] is a commutative associative algebra, which is called the derivation Lie algebra of its derivative as Witt algebra, and it is recorded as a Wd. quantum torus algebra Cq is a noncommutative associative algebra similar to Ad, and its derivate Lie algebra is recorded as Der (Cq) when d=2, Witt algebra W2 has a natural subalgebra L=L2 and after removing the subalgebra of subalgebra. The natural subalgebra G (q) of Der (q) = L2 (q), L (q) = L2 (q) is q-Virasoro-like algebra.1986 year. Shen Guangyu defines a class of weights, and the function of the unit matrix is constant. The structure of this class of weights is depicted. When d=2, Fb alpha (V) can be considered as a model on Virasoro-like algebra. Similarly, we can define the modulus Fq alpha (V) on q-Virasoro-like algebra. In this paper, we study the irreducibility of these modules in a unified way. The main fruit is: (1) we have determined the irreducibility of Fb a (V). When the weight space V is infinite dimension, we get a new class of Irreducible Modules on the infinite dimension of the weight space on Virasoro-like algebra; (2) no matter whether V is finite or infinitely irreducible s[2 module, the mode Fq alpha (V) can be decomposed into a direct sum of an irreducible submode and another submode, and we also determine the irreducibility of another submode. Besides, We also characterize the structure of the modulus of freedom of C[(?) 1, (?) 2]- on algebraic L, which is isomorphic to Q (2, alpha).

【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O152.5
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本文编号：1800789