Leibniz algebras with low-dimensional maximal Lie quotients. (English) Zbl 1477.17017

Summary: 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.


17A32 Leibniz algebras
17A60 Structure theory for nonassociative algebras
Full Text: DOI


[1] 10.1080/00927872.2012.717655 · Zbl 1306.17001
[2] 10.2140/involve.2011.4.293 · Zbl 1252.17003
[3] 10.1090/conm/623/12456
[4] 10.1007/1-84628-490-2
[5] 10.5169/seals-60428
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