具有二维偶数部分的奇异超代数的结构和奇异超代数的新实例

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2023-11-08 DOI:10.1007/s10469-023-09716-z

S. V. Pchelintsev, O. V. Shashkov

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引用次数: 0

摘要

研究证明，具有 2 维偶数部分的奇异超代数与超代数 B2|3(φ,ξ,ψ)同构。特别是，不存在具有 2 维偶数部分的无限维简单奇异超代数。证明了如果奇异超代数包含一个奇数左湮没器，那么它就包含一个非enerate 开关。最后，证明了对于任何 N ≥ 5 的数，除了 6、7、8、11 以外，都存在具有 N 维开关的奇异超代数；对于 N = 6、7、8、11 的数，不存在具有开关的 N 维奇异超代数。

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Structure of Singular Superalgebras with 2-Dimensional Even Part and New Examples of Singular Superalgebras

It is proved that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra B_2|3(φ, ξ, ψ). In particular, there do not exist infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number N ≥ 5, except the numbers 6, 7, 8, 11, there exist singular superalgebras with a switch of dimension N. For the numbers N = 6, 7, 8, 11, there do not exist singular N -dimensional superalgebras with a switch.

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.