共查询到20条相似文献,搜索用时 15 毫秒
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The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm
must be isomorphic toW(m,n, 1) if the dimension ofG
i satisfies a certain condition.
Project supported by the National Natural Science Foundation of China and the Science of the University Doctoral Program of
CNEC. 相似文献
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D. A. Leites 《Journal of Mathematical Sciences》1985,30(6):2481-2512
Results pertaining to the theory of representations of classical Lie superalgebras are collected in the survey.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 25, pp. 3–50, 1984. 相似文献
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In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras. These results are used later to affirmatively answer questions, which were originally posed in Boe et al. (2010) [5] and Bagci et al. (2008) [2], about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras. 相似文献
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I. B. Penkov 《Journal of Mathematical Sciences》1990,51(1):2108-2140
The paper is devoted to a systematic construction of the elements of Borel-Weil-Bott theory in the supercase. The main result is a presentation of the cohomology of typical irreducible G-sheaves on G/B, where G is the connected component of the identity in a classical complex Lie supergroup and B G an arbitrary Borel subsupergroup. Also presented are some simple known results concerning the cohomology of irreducible G-sheaves on G/P for a parabolic subsupergroup P.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 32, pp. 71–124, 1988. 相似文献
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In this paper, we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations. Finally, we study the linear super commuting maps on the centerless super-Virasoro algebras. 相似文献
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Yu Wang 《Linear and Multilinear Algebra》2016,64(8):1518-1526
The aim of this paper is to investigate Lie superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we obtain a definitive result on Lie superderivations of prime superalgebras. 相似文献
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The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra. 相似文献
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Yuri Bahturin Susan Montgomery 《Proceedings of the American Mathematical Society》1999,127(10):2829-2839
In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.
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George McNinch 《Transformation Groups》2007,12(1):127-135
Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a
G-completely reducible subgroup H ⊂ G. In this paper, we give a notion of G-complete reducibility—G-cr for short—for Lie subalgebras
of Lie(G), and we show that if the closed subgroup H ⊂ G is G-cr, then Lie(H) is G-cr as well. 相似文献
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Lisun Zheng 《代数通讯》2017,45(6):2417-2434
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Mingzhong WU 《Frontiers of Mathematics in China》2015,10(3):697
We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of D e r 0 ˉ (Ln,m) and D e r 1 (Ln,m). By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra. 相似文献
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