共查询到17条相似文献,搜索用时 500 毫秒
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带有非退化不变对称双线性型的有限维可解李代数 总被引:3,自引:0,他引:3
本文讨论复数域上带有非退化不变对称双线性型的,可裂的有限维可解李代数的性质及结构.给出了不可分解的非退化可解李代数的定义.证明了本文所讨论的李代数可以分解成不可分解的非退化可解理想的正交直和.对于不可分解的非退化可解李代数,给出了它关于极大环面子代数的根空间分解;讨论了根空间的结构及运算关系;证明了它的 Cartan 子代数的交换性,并给出了 Cartan子代数的结构. 相似文献
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讨论了二次李超三系的唯一分解,得到了二次李超三系分解为非退化不可约阶化理想的分解定理. 相似文献
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代数A称为不可分解的,如果A不能分解成理想的直和.满足C(Lo)=C(L)={0}的Jordan李超代数L能够分解成不可分解理想的直和,这种分解在不计理想次序的前提下是唯一的.并证明了完备Jordan李超代数的一些性质. 相似文献
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代数$A$ 称为不可分解的,如果 $A$ 不能分解成理想的直和.文中将证明满足$C(L_{\bar{0}})=C(L)=\{0\}$的限制李超代数能够分解成不可分解限制理想的直和,这种分解在不计理想次序的前提下是唯一的.而且还证明了限制李超代数的一些结果. 相似文献
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考察了辛代数和与它相联系的李三系的双线性型之间的关系,并证明了辛代数的反对称不变双线性型可以唯一扩张到与它相联系的李三系中.作为这种关系的一个应用,得到了二次辛代数是单辛代数的一个充要条件,并证明二次辛代数的唯一分解定理. 相似文献
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本文考察了反李三系和它的标准嵌入李超代数的Killing型之间的关系,并且证明了反李三系的反对称不变双线性型可以被唯一地扩张到它的标准嵌入李超代数。作为扩张定理的一个应用,得到了二次李和反李三系的唯一分解定理。 相似文献
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本文讨论李三系的可解根基和Hopkins幂零的某些性质及导子作用下的不变性,讨论了李三系次理想的某些性质,证明了李三系为幂零的当且仅当每个子系都是次理想. 相似文献
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《代数通讯》2013,41(11):5145-5154
In this paper, we consider the decomposition of a quadratic Lie algebra and the main result is that the decomposition of a quadratic Lie algebra into irreducible nondegenerate ideals is unique up to an isometry (Theorem 3.1). As a corollary, we obtain the uniqueness of the decomposition of an arbitrary Lie algebra into indecomposable ideals up to an isomorphism (Corollary 3.5.4). 相似文献
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Uniqueness of the decomposition of lie superalgebras and quadratic lie superalgebras 总被引:1,自引:0,他引:1
A Lie superalgebra endowed with a non-degenerate super-symmetric and invariant bilinear form is called a quadratic Lie superalgebra. ln this paper, we consider the decomposition of a Lie superalgebra and the first main result is that the decomposition of a Lie superalgebra into indecomposable graded ideals is unique up to an isomorphism. Next, we obtain the uniqueness of the decomposition of an arbitrary quadratic Lie superalgebra into irreducible graded ideals up to an isometry. 相似文献
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Cristina Draper Antonio Fernández López Esther García Miguel Gómez Lozano 《Journal of Algebra》2008,319(6):2372-2394
We define the socle of a nondegenerate Lie algebra as the sum of all its minimal inner ideals. The socle turns out to be an ideal which is a direct sum of simple ideals, and satisfies the descending chain condition on principal inner ideals. Every classical finite dimensional Lie algebra coincides with its socle, while relevant examples of infinite dimensional Lie algebras with nonzero socle are the simple finitary Lie algebras and the classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space. This notion of socle for Lie algebras is compatible with the previous ones for associative algebras and Jordan systems. We conclude with a structure theorem for simple nondegenerate Lie algebras containing abelian minimal inner ideals, and as a consequence we obtain that a simple Lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank-one element. 相似文献
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代数A称为不可分解的,如果A不能分解成理想的直和.证明了满足C(L_o)=C(L)={0}的Jordan李超代数L一些重要性质. 相似文献
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In this article, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems. 相似文献
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Nora C. Hopkins 《代数通讯》2013,41(8):2231-2237
We analyze how certain constructions of Lie module triple systems affect the structure theory, particularly simplicity. We are thus able to show that there is no upper bound on the number of summands in a direct sum decomposition of a simple Lie module triple system as a module for its inner derivation algebra. 相似文献
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It is proved that an Artinian Noetherian module over a ring with involution on which there is defined a nondegenerate antisymmetric invariant bilinear form decomposes into a direct sum of pairwise orthogonal summands, each of which is either indecomposable or a direct sum of two indecomposable modules. This theorem had been previously proved for such modules with unique division by 2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 28–31, 1982. 相似文献