$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras

Ruipu Bai; Yansha Gao; Zhenheng Li

$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras

Rings and Algebras 2016-07-29 v1

Authors: Ruipu Bai , Yansha Gao , Zhenheng Li

Abstract

We study an extension algebra $A$ from two given $3$ -Lie algebras $M$ and $H$ , and discuss the extensibility of a pair of derivations, one from the derivation algebra of $M$ and the other from that of $H$ , to a derivation of $A$ . In particular, we give conditions for such an extension to be a $3$ -Lie algebra, and provide necessary and sufficient conditions of the pair of derivations to be extendable.

Keywords

3-Lie algebras extension algebra derivation derivation algebra pair of derivations extensibility necessary and sufficient conditions

Cite

@article{arxiv.1607.08276,
  title  = {$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras},
  author = {Ruipu Bai and Yansha Gao and Zhenheng Li},
  journal= {arXiv preprint arXiv:1607.08276},
  year   = {2016}
}

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24 pages

$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras

Abstract

Keywords

Cite

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