Derivation Lie algebras of semidirect sums

Abstract

Suppose that \(L=L_1 \ltimes L_2\) is a semidirect sum of two Lie algebras. In this article, we first obtain the structure of \({\text {Der}}(L:L_2)\) the subalgebra of \({\text {Der}}(L)\) that consists of those derivations mapping \(L_2\) to itself. Then we investigate some conditions under which \({\text {Der}}(L:L_2)\) is also a semidirect sum.

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Correspondence to F. Saeedi.

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Barati, M., Saeedi, F. & Alemi, M.R. Derivation Lie algebras of semidirect sums. Rend. Circ. Mat. Palermo, II. Ser 69, 653–663 (2020). https://doi.org/10.1007/s12215-019-00424-1

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Keywords

  • Semidirect sum
  • Derivation
  • Cohomology of Lie algebra

Mathematics Subject Classification

  • Primary 17B40
  • 17B56
  • Secondary 18G60