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Structure of -Lie Algebras with Involutive Derivations

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  • Ruipu Bai
  • Shuai Hou
  • Yansha Gao

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.

Suggested Citation

  • Ruipu Bai & Shuai Hou & Yansha Gao, 2018. "Structure of -Lie Algebras with Involutive Derivations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-9, September.
    • Handle: RePEc:hin:jijmms:7202141
    DOI: 10.1155/2018/7202141
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