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