共查询到20条相似文献,搜索用时 15 毫秒
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Michael Peretzian Williams 《代数通讯》2013,41(6):1843-1849
We find examples of nilpotent n-Lie algebras and prove n-Lie analogs of classical group theory and Lie algebra results. As an example we show that a nilpotent ideal I of class c in a n-Lie algebra A with A/I 2 nilpotent of class d is nilpotent and find a bound on the class of A. We also find that some classical group theory and Lie algebra results do not hold in n-Lie algebras. In particular, non-nilpotent n-Lie algebras can admit a regular automorphism of order p, and the sum of nilpotent ideals need not be nilpotent. 相似文献
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Wolfgang Alexander Moens 《代数通讯》2013,41(7):2427-2440
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. The proofs are elementary in nature and are based on well-known techniques. We only consider finite-dimensional Lie algebras over a fields of characteristic zero. 相似文献
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It is proved that if a (?/p ?)-graded Lie algebra L, where p is a prime, has exactly d nontrivial grading components and dim L 0 = m, then L has a nilpotent ideal of d-bounded nilpotency class and of finite (m,d)-bounded codimension. As a consequence, Jacobson's theorem on constant-free nilpotent Lie algebras of derivations is generalized to the almost constant-free case. Another application is for Lie algebras with almost fixed-point-free automorphisms. 相似文献
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In this article, we introduce the notion of the equivalence relation, n-isoclinism, between Lie algebras, and obtain some criterions under which Lie algebras are n-isoclinic. In particular, we show that n-isoclinic Lie algebras can be isoclinically embedded into one Lie algebra. Also, we present the notion of an n-stem Lie algebra and prove its existence within an arbitrary n-isoclinism class. In addition, similar to a result of Hekster [6] in the group case, we characterize the n-stem Lie algebras in the n-isoclinism classes which contains at least one finitely generated Lie algebra L with dim (L n+1) finite. 相似文献
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Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R = R ?? L ? be a Chevalley algebra of type L over a commutative ring R. Let 𝒩(R) be the nilpotent subalgebra of L R spanned by the root vectors associated with positive roots. A map ? of 𝒩(R) is called commuting if [?(x), x] = 0 for all x ∈ 𝒩(R). In this article, we prove that under some conditions for R, if Φ is not of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a central derivation (resp., automorphism), and if Φ is of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a sum (resp., a product) of a graded diagonal derivation (resp., automorphism) and a central derivation (resp., automorphism). 相似文献
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Constantinos E. Kofinas 《代数通讯》2013,41(4):1575-1593
Let L be a relatively free nilpotent Lie algebra over ? of rank n and class c, with n ≥ 2; freely generated by a set 𝒵. Give L the structure of a group, denoted by R, by means of the Baker–Campbell–Hausdorff formula. Let G be the subgroup of R generated by the set 𝒵 and N Aut(L)(G) the normalizer in Aut(L) of the set G. We prove that the automorphism group of L is generated by GL n (?) and N Aut(L)(G). Let H be a subgroup of finite index in Aut(G) generated by the tame automorphisms and a finite subset X of IA-automorphisms with cardinal s. We construct a set Y consisting of s + 1 IA-automorphisms of L such that Aut(L) is generated by GL n (?) and Y. We apply this particular method to construct generating sets for the automorphism groups of certain relatively free nilpotent Lie algebras. 相似文献
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Hannes Pouseele 《Geometriae Dedicata》2006,122(1):77-88
We discuss three general problems concerning the cohomology of a (real or complex) nilpotent Lie algebra: first of all, determining
the Betti numbers exactly; second, determining the distribution these Betti numbers follow; and finally, estimating the size
of the individual cohomology spaces or the total cohomology space. We show how spectral sequence arguments can contribute
to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers
exactly. We then show that some families in this class have a M-shaped Betti number distribution, and construct the first
examples with an even more exotic Betti number distribution. Finally, we discuss the construction of (co)homology classes
for split metabelian Lie algebras, thus proving the Toral Rank Conjecture for this class of algebras. 相似文献
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Maria V. Milentyeva 《代数通讯》2013,41(4):1141-1154
We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also compute a similar function for complex nilpotent Lie groups of class 2. 相似文献
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本文讨论了完备李代数的同构问题,并对幂零根基为一些Heisenberg代数及交换李代数之直和的可解和一般完备李代数的结构进行了讨论. 相似文献
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Binyong Hsie 《代数通讯》2013,41(10):3743-3750
In this article, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete. 相似文献
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Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues of the maximal nilpotent Lie subalgebras of finite-dimensional simple Lie algebras. In this article, we use Hodge Laplacian to study the cohomology of these Lie algebras. The “total rank conjecture” and “b 2-conjecture” for the algebras are proved. Moreover, we find the generating functions of the Betti numbers by means of Young tableaux for the Lie algebras associated with certain tree diagrams of single branch point. By these functions and Euler–Poincaré principle, we obtain analogues of the denominator identity for finite-dimensional simple Lie algebras. The result is a natural generalization of the Bott's classical result in the case of special linear Lie algebras. 相似文献
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A. Shabanskaya 《代数通讯》2013,41(8):3626-3667
A pair of sequences of nilpotent Lie algebras denoted by Nn, 7 and Nn, 16 are introduced. Here, n denotes the dimension of the algebras that are defined for n ≥ 6; the first terms in the sequences are denoted by 6.7 and 6.16, respectively, in the standard list of six-dimensional Lie algebras. For each of them, all possible solvable extensions are constructed so that Nn, 7 and Nn, 16 serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time. 相似文献
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We determine the moduli space of metric two-step nilpotent Lie algebras of dimension up to 6. This space is homeomorphic to
a cone over a four-dimensional contractible simplicial complex. Moreover, we exhibit standard metric representatives of the
seven isomorphism types of six-dimensional two-step nilpotent Lie algebras within our picture.
Mathematics Subject Classifications (2000): Primary 22E25, 53C30, 22E60 相似文献
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Zsolt Balogh 《代数通讯》2013,41(2):315-324
In this article the Lie derived length and the strong Lie derived length of group algebras are determined in the case when the derived subgroup of the basic group is cyclic of odd order. As a consequence, we have the characterization of the group algebras of minimal strong Lie derived length. 相似文献
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介绍了李color代数的T*-扩张的定义,并证明李color代数的很多性质,如幂零性、可解性和可分解性,都可以提升到它的T*-扩张上.还证明在特征不等于2的代数闭域上,有限维幂零二次李color代数A等距同构于一个幂零李color代数B的T*-扩张,并且B的幂零长度不超过A的一半.此外,用上同调的方法研究了李color代数的T*-扩张的等价类. 相似文献