Geoffrey Mason, Gaywalee Yamskulna, “Leibniz Algebras and Lie Algebras”, SIGMA, 2013, Volume 9,063, 10 pp.

This article is cited in 18 papers

Leibniz Algebras and Lie Algebras

Geoffrey Mason^a, Gaywalee Yamskulna^bc

^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

Abstract: 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.

Keywords: Leibniz algebras; Lie algebras.

MSC: 17A32

Received: September 9, 2013; in final form October 19, 2013; Published online October 23, 2013

Language: English

DOI: 10.3842/SIGMA.2013.063