共查询到19条相似文献,搜索用时 78 毫秒
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通过δ-Jordan李超代数T的表示和上同调理论,构造δ-Jordan李超代数T■V.证明了δ-Jordan李超代数的等价交换扩张给出相同的表示.通过δ-Jordan李超代数的表示和其交换扩张得到2-上圈. 相似文献
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利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系. 相似文献
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利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系. 相似文献
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孙昌璞 《数学物理学报(A辑)》1991,11(2):121-129
本文从普遍的代数观点出发,考虑到李超代数的Boson-Fermion实现,研究了任意李超代数在Heisenberg-Weyl超代数的通用包络代数相关空间上的无穷维不可分解表示。在特定的商空间上,这个表示将诱导出各种有限维表示,通常的不可约表示仅作为特殊情况给出。作为具体例子,我们给出了典型李超代数Gsl(2)(B(0,1),在耦合基下的不可分解表示。最后,我们证明了荷载这种无穷维不可分解表示的商空间同构于物理空间——广义Fock空间。 相似文献
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着色李超代数与左着色对称结构 总被引:1,自引:0,他引:1
本文研究了着色李超代数上的左着色对称结构问题.利用着色李超代数的两种仿射表示和1-上同调群,得出左着色对称结构存在的几个充分或必要条件,推广了文[2]的结论. 相似文献
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主要研究了复数域上的特殊线性李超代数sl(m,n)的型心与拟型心,其中m+n=4.应用解线性方程组的方法,完全确定了这些李超代数型心和拟型心的矩阵表示. 相似文献
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对经典文献中李超代数的Schur引理的各种表述进行比对研究.给出李超代数的Schur引理的明晰表达及证明;作为应用,刻画了一类Heisenberg李超代数的不可约模的自同态.进而利用奇偶函子和符号映射刻画了李超代数模同态的各种定义之间的关系. 相似文献
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The purpose of this article is to study cohomology and representations of Bihom-Lie superalgebras. In particular, trivial representations and adjoint representations of Bihom-Lie superalgebras are studied in detail. Derivations and central extensions of Bihom-Lie superalgebras are also discussed as an application. 相似文献
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Shujuan Wang 《Linear and Multilinear Algebra》2016,64(10):2081-2089
Over an algebraically closed field of characteristic zero, all the abelian subalgebras of maximal dimensions for the general linear Lie superalgebras are classified in the sense of conjugation. As a consequence, the minimal faithful representations are determined for the so-called nice abelian Lie superalgebras. 相似文献
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This paper is primarily concerned with δ-Hom-Jordan Lie superalgebras. We discuss the concepts of αk-derivations, representations and T*-extensions of δ-Hom-Jordan Lie superalgebras in detail, and some cohomological characterizations are established. 相似文献
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We provide a systematic approach to obtain formulas for characters and Kostant u-homology groups of the oscillator modules of the finite-dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite-dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highest weight representations of Hermitian symmetric pairs. In addition, two new reductive dual pairs related to the above-mentioned u-homology computation are worked out. 相似文献
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Xu Xiang 《数学学报(英文版)》1997,13(2):161-168
In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations
of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all
weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras
are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations.
This work was supported by CNSF 相似文献
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Shujuan Wang 《Linear and Multilinear Algebra》2016,64(7):1354-1361
This paper determines the minimal dimensions of faithful representations for abelian Lie superalgebras of finite dimensions over an algebraically closed field of characteristic zero. In particular, we also obtain the maximal dimensions of abelian subalgebras for the general linear Lie superalgebras. 相似文献
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This paper is a survey of results on representations of alternative algebras and superalgebras. In particular, new results of the authors on the subject are presented. 相似文献
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Over an algebraically closed field of characteristic zero, all the abelian subalgebras of the maximal dimension are classified for any special Jordan algebra. As a consequence, the minimal dimension of the faithful representations of any finite-dimensional abelian Jordan algebra is determined and the minimal faithful representations are classified for the so-called nice abelian Jordan algebras. The same is done for the purely odd Lie superalgebras. 相似文献
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Emanuela Petracci 《Bulletin des Sciences Mathématiques》2003,127(5):439-465
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincaré-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras. 相似文献