Vol. 12, No. 5, 2019

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Leibniz algebras with low-dimensional maximal Lie quotients

William J. Cook, John Hall, Vicky W. Klima and Carter Murray

Vol. 12 (2019), No. 5, 839–853
Abstract

Every Leibniz algebra has a maximal homomorphic image that is a Lie algebra. We classify cyclic Leibniz algebras over an arbitrary field. Such algebras have the 1-dimensional abelian Lie algebra as their maximal Lie quotient. We then give examples of Leibniz algebras whose associated maximal Lie quotients exhaust all 2-dimensional possibilities.

Keywords
Leibniz algebra, cyclic Leibniz algebra, low-dimensional examples
Mathematical Subject Classification 2010
Primary: 17A32
Secondary: 17A60
Milestones
Received: 31 August 2018
Revised: 9 October 2018
Accepted: 1 January 2019
Published: 22 May 2019

Communicated by Ravi Vakil
Authors
William J. Cook
Department of Mathematical Sciences
Appalachian State University
Boone, NC
United States
John Hall
Department of Mathematics
University of Kentucky
Lexington, KY
United States
Vicky W. Klima
Department of Mathematical Sciences
Appalachian State University
Boone, NC
United States
Carter Murray
Department of Mathematical Sciences
Appalachian State University
Boone, NC
United States