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71.
利用复数域C上四维Filiform李超代数的分类,通过计算刻画了复数域C上四维Filiform李超代数上的所有Yang-Baxter方程的解. 相似文献
72.
73.
In [1], the second de Rham cohomology groups of nilpotent orbits in all the complex simple Lie algebras are described. In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the above computations, we obtain upper bounds for the dimensions of the second cohomology groups. 相似文献
74.
Mohsen Parvizi 《代数通讯》2013,41(6):2287-2294
75.
Karl Lorensen 《代数通讯》2013,41(12):4345-4364
76.
77.
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
78.
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
79.
Alon Regev 《代数通讯》2013,41(3):772-781
Amitsur proved the following theorem for an uncountable field k: Let A be a k-algebra, then any finite-dimensional nil subspace of A has bounded index, and any finite dimensional algebraic subspace of A has bounded degree. Here we give a new proof of Amitsur's theorem, a proof which is more elementary and direct, than Amitsur's original proof. 相似文献
80.
In this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among their isomorphism classes. In particular, we prove that 𝒥2 and 𝒥3 are irreducible and that 𝒥4 is the union of the Zariski closures of the orbits of two rigid Jordan algebras. 相似文献