Leibniz superalgebras and central extensions

Details Leibniz superalgebras and central extensions Leibniz superalgebras and central extensions

2005-10-26

arxiv.org/abs/math/0510546v1

Published in Journal algebra and its Applications, Vol.5, No.6(2006),765-780

Mathematics

Representation Theory

19 pages

Scientific paper

Dialgebras are generalizations of associative algebras which give rise to Leibniz algebras instead of Lie algebras. In this paper we study super dialgebras and Leibniz superalgebras, which are $\z_2$-graded dialgebras and Leibniz algebras. We also study universal central extesions of Leibniz superalgebras and obtain some results as in the case of Lie superalgebras. We determine universal central extensions of basic classical Lie superalgebras in the category of Leibniz superalgebras. They play a key role in studying Leibniz superalgebras graded by finite root systems.

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