有限群上乘法李代数结构的分类

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2021-01-01 DOI:10.4064/cm8397-12-2020

Mani Shankar Pandey, S. Upadhyay

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引用次数: 3

摘要

．群G上的每一个乘法李代数结构决定了从外方G∧G到G的群同态。我们给出了G上的群同态G∧G→G的精确刻画，这群同态决定了G上的一个乘法李代数结构。对于某些有限群，我们确定了这种结构定义映射的可能象的数目(直到同构)。

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Classification of multiplicative Lie algebra structures on a finite group

. Every multiplicative Lie algebra structure on a group G determines a group homomorphism from the exterior square G ∧ G to G . We give a precise character-ization of the group homomorphisms G ∧ G → G which determine a multiplicative Lie algebra structure on G . For certain ﬁnite groups, we determine the number of possible images (up to isomorphism) of such structure-deﬁning maps.

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.