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