共查询到20条相似文献,搜索用时 15 毫秒
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Isao Kikumasa Kiyoichi Oshiro Hiroshi Yoshimura 《Applied Categorical Structures》2008,16(1-2):297-310
We study to classify, up to isomorphism, algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. The number of local quasi-Frobenius k-algebras with the condition is shown to be not less than the cardinality of k. In particular, the canonical forms of those algebras of dimension 5 are presented and their isomorphism classes are completely
determined under some conditions on k.
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In this article, we prove that, for a radical square zero algebra A given by a finite quiver Q without multiple arrows, the twisted double of A is cellular if and only if Q has no cycles. 相似文献
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Complete Commutative Basic Algebras 总被引:1,自引:0,他引:1
By a basic algebra is meant an MV-like algebra (A, ⊕, ¬, 0) of type 〈2, 1, 0〉 derived in a natural way from bounded lattices having antitone involutions on their principal filters. In the previous paper (Botur and Hala?, Mult. Valued Log. Soft Comp., 2007) we have shown that finite basic algebras for which the operation ⊕ is commutative are MV-algebras. In this paper we generalize this result by considering commutative basic algebras for which the underlying lattice is complete. 相似文献
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Juan C. Gutierrez Fernandez A. Grishkov Mary L. R. Montoya Lucia S. I. Murakami 《代数通讯》2013,41(9):3151-3165
The aim of this article is to study the structure of the modules over a trivial algebra of dimension two in the variety ? of commutative and power-associative algebras. In particular, we classify the irreducible modules. These results enables us to understand better the structure of finite-dimensional power-associative algebras of nilindex 4. 相似文献
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The category of all two-dimensional real commutative division algebras is shown to split into two full subcategories. One
of them is equivalent to the category of the natural action of the cyclic group of order 2 on the open right half plane . The other one is equivalent to the category of the natural action of the dihedral group of order 6 on the set of all ellipses
in which are centered at the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions
are easily described. Together with they classify all real commutative division algebras up to isomorphism. Moreover we describe all morphisms between the objects
in this classifying set, thus obtaining a complete picture of the category of all real commutative division algebras, up to
equivalence. This supplements earlier contributions of Kantor and Solodovnikov, Hypercomplex Numbers: An Elementary Introduction to Algebras, Nauka, Moscow, 1973; Benkart et al., Hadronic J., 4: 497–529, 1981; and Althoen and Kugler, Amer. Math. Monthly, 90: 625–635, 1983, who achieved partial results on the classification of the real commutative division algebras.
Dedicated to Claus Michael Ringel on the occasion of his 60th birthday. 相似文献
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A commutative fusion algebra is proved to be amenable if and only if the associated regular representation is bounded. 相似文献
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Christakis A. Pallikaros 《代数通讯》2013,41(11):4839-4859
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Zhengxin Chen 《代数通讯》2013,41(2):738-769
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 with identity. Let ?(R) be the solvable subalgebra of L R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ?(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ?(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ?(R) are determined. 相似文献
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给出了三角代数上交换零点Jordan可导映射的结构.作为应用,得到了套代数上交换零点Jordan可导映射的具体形式. 相似文献
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We introduce the notion of domain for Lie algebras, discuss when the free amalgamated Lie product of two domains is a domain again, classify commuting elements in the free amalgamated product of two Lie algebras and describe the center of this product. 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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E. N. Poroshenko 《代数通讯》2013,41(2):746-762
In this paper, we consider partially commutative metabelian Lie algebras whose defining graphs are cycles. We show that such algebras are universally equivalent iff the corresponding cycles have the same length. Moreover, we give an example showing that the class of partially commutative metabelian Lie algebras such that their defining graphs are trees is not separable by universal theory in the class of all partially commutative metabelian Lie algebras. 相似文献