On Schur Multiplier of a Pair of Lie Algebras

Document Type : Research Paper

Author

Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.

Abstract

Nilpotent Lie algebras have played an important role in mathematics in the classification theory of
Lie algebras. Let (N, L) be a pair of finite dimensional Lie algebras. Let K be an ideal of L such
that L = N ⊕ K and N be a filiform ideal of L. Also, let dim N = n and dim K = m. Then
s′(N, L) = 1/2(n − 1)(n − 2) + 1 + (n − 1)m − dim M(N, L). In this paper, we characterize the pair
(N, L) for s′(N; L) = 0, 1, 2,..., 15.

Keywords

References

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Global Analysis and Discrete Mathematics
Volume 7, Issue 2
September 2022
Pages 161-169

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History

  • Receive Date: 03 May 2022
  • Revise Date: 27 December 2022
  • Accept Date: 01 March 2023

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