Isotopism and Isomorphism Classes of Certain Lie Algebras over Finite Fields

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• 作者：O. J. Falcón ; R. M. Falcón ; J. Núñez
• 关键词：Lie algebra ; isotopism ; isomorphism
• 刊名：Results in Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：71
• 期：1-2
• 页码：167-183
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-9012
• 卷排序：71

文摘

In the current paper, we study the distribution into isotopism and isomorphism classes of the relevant family \({\mathcal{F}_n^p}\) of Lie algebras of basis \({\{e_1,\ldots,e_n\}}\) and nonzero brackets \({[e_i, e_n] \in \langle\,e_1,\ldots,e_{n-1}\,\rangle}\) over a finite field \({\mathbb{F}_p}\), with p prime. At this end we first introduce the concept of the structure tuple of a Lie algebra and specifically prove that there exist n isotopism classes in \({\mathcal{F}_n^p}\) and three families of isomorphism classes depending on the first component of their structure tuple.