Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 063, 10 pages      arXiv:1201.5071
Contribution to the Special Issue on New Directions in Lie Theory

Leibniz Algebras and Lie Algebras

Geoffrey Mason a and Gaywalee Yamskulna b, c
a) Department of Mathematics, University of California, Santa Cruz, CA 95064, USA
b) Department of Mathematical Sciences, Illinois State University, Normal, IL 61790, USA
c) Institute of Science, Walailak University, Nakon Si Thammarat, Thailand

Received September 09, 2013, in final form October 19, 2013; Published online October 23, 2013

This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.

Key words: Leibniz algebras; Lie algebras.

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