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Leibniz A -algebras

David A. Towers (2020)

Communications in Mathematics

A finite-dimensional Lie algebra is called an A -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.

Local superderivations on Lie superalgebra 𝔮 ( n )

Haixian Chen, Ying Wang (2018)

Czechoslovak Mathematical Journal

Let 𝔮 ( n ) be a simple strange Lie superalgebra over the complex field ℂ . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over ℂ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but 𝔭 ( n ) is an exception. In this...

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