Structure of -Lie Algebras with Involutive Derivations

Ruipu Bai, Shuai Hou and Yansha Gao

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-9

Abstract:

We study the structure of -Lie algebras with involutive derivations for . We obtain that a -Lie algebra is a two-dimensional extension of Lie algebras if and only if there is an involutive derivation on such that or , where and are subspaces of with eigenvalues and , respectively. We show that there does not exist involutive derivations on nonabelian -Lie algebras with for . We also prove that if is a -dimensional -Lie algebra with , then there are involutive derivations on if and only if is even, or satisfies . We discuss also the existence of involutive derivations on -dimensional -Lie algebras.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7202141

DOI: 10.1155/2018/7202141

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