可解莱布尼兹超代数中的阿贝尔子代数和最大维度的理想数

IF 1.1 3区数学 Q1 MATHEMATICS Mediterranean Journal of Mathematics Pub Date : 2024-04-06 DOI:10.1007/s00009-024-02634-z

Sofiane Bouarroudj, Antonio J. Calderón, Amir Fernández Ouaridi, Rosa María Navarro

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引用次数: 0

摘要

我们在莱布尼兹超代数的背景下研究了与最大维度的无方子代数（理想）的维度相对应的常（α）和（β）。我们证明，如果存在一个标度为一的无性子代数，这些不变式是重合的。我们还研究了最大维度的无性子代数的维度为二的情况。最后，我们研究了莱布尼兹超代数一些杰出族的（α）和（β）不变式。

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Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

We study the invariants \(\alpha \) and \(\beta \), which correspond to the dimension of an abelian subalgebra (ideal resp.) of maximal dimension, in the context of Leibniz superalgebras. We prove that these invariants coincide if there is an abelian subalgebra of codimension one. We also examine the case in which the abelian subalgebras of maximal dimension are of codimension two. Finally, we study the \(\alpha \) and \(\beta \) invariants for some distinguished families of Leibniz superalgebras.

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.