共查询到17条相似文献,搜索用时 93 毫秒
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本文将模李代数中环面与环面秩的理论推广到模李超代数中.应用模李超代数的限制包络得到了环面秩的若干重要性质.作为应用,计算了典型李超代数slm|n与限制Cartan型李超代数W(m,n,1),S(m,n,1)的绝对环面秩及S(m,n,1)在W(m,n,1)中的环面秩. 相似文献
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设W(m,n)是特征p3的代数闭域上有限维Witt型李超代数.证明了W(m,n)的极大根阶化子代数一定是其极大Z-阶化子代数,从而刻画了W(m,n)的所有极大根阶化子代数.结果有助于理解Witt型李超代数W(m,n)的内在性质. 相似文献
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构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数. 相似文献
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Cartan型广义李超代数 总被引:1,自引:0,他引:1
设F是特征不为2的域.本文定义了F上的广义李超代数,证明了Z-阶化广义李超代数的单性准则.然后定义了有限维Cartan型广义李超代数W(n),证明了W(n)的单性.最后指出对Cartan型广义李超代数S(n)与H(n),亦有与W(n)相似的结果. 相似文献
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本文构造了有限维模李超代数(-W).利用已有的模李超代数W(m,n,t_),证明了(-W)是单李超代数,获得了(-W)是限制李超代数的一个充分必要条件,进而证明了-W没有非退化结合型. 相似文献
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董泉发 《数学年刊A辑(中文版)》2015,36(3):325-334
构造了Cartan型李代数W(n;m)的一类Borel子代数φ(n;m),其中n是一个正整数,且m=(m_1,…,m_n)是一个n-元正整数数组.确定了φ(n;m)的导子代数.特别地,φ(n;1)是一个Cartan型完备阶化李代数,它不同于任何典型完备李代数. 相似文献
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有限维单Cartan型模李超代数HO 总被引:4,自引:0,他引:4
本文构造了一族有限维Cartan型模李超代数-奇Hamilton模李超代数HO, 并证明了其单性.通过建立Cartan型模李超代数W,H,K,S和HO的维数公式,讨 论了奇Hamilton模李超代数HO与Cartan型模李超代数W,S,H,K的同构关系. 相似文献
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本文给出了Z-阶化有限维单李超代数具有非退化亦型的一个必要条件。应用这一结果,我们可以得到Cartan型李超代数X(n)与X(m,n,t)的Killing型是退化的。 相似文献
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S. Bouarroudj P. Ya. Grozman D. A. Leites 《Functional Analysis and Its Applications》2008,42(3):161-168
Over algebraically closed fields of characteristic p > 2, —prolongations of simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. We discover several new simple Lie superalgebras, serial and exceptional, including super versions of Brown and Melikyan algebras, and thus corroborate the super analog of the Kostrikin-Shafarevich conjecture. Simple Lie superalgebras with 2 × 2 Cartan matrices are classified. 相似文献
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The authors consider a family of finite-dimensional Lie superalgebras of O-type
over an algebraically closed field of characteristic p > 3. It is proved that the Lie superalgebras
of O-type are simple and the spanning sets are determined. Then the spanning
sets are employed to characterize the superderivation algebras of these Lie superalgebras.
Finally, the associative forms are discussed and a comparison is made between these Lie
superalgebras and other simple Lie superalgebras of Cartan type. 相似文献
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Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra. 相似文献
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For the Kac-Moody superalgebra associated with the loop superalgebra with values in a finite-dimensional Lie superalgebra
g, we show what its quadratic Casimir element is equal to if the Casimir element for g is known (if g has an even invariant
supersymmetric bilinear form). The main tool is the Wick normal form of the even quadratic Casimir operator for the Kac-Moody
superalgebra associated with g; this Wick normal form is independently interesting. If g has an odd invariant supersymmetric
bilinear form, then we compute the cubic Casimir element. In addition to the simple Lie superalgebras g = g(A) with a Cartan
matrix A for which the Shapovalov determinant was known, we consider the Poisson Lie superalgebra poi(0|n) and the related
Kac-Moody superalgebra.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 378–397, September, 2008. 相似文献
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