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

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

Involve 12, No. 5, 839-853 (2019).
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.

Cited in 1 Document

MSC:

17A32 Leibniz algebras
17A60 Structure theory for nonassociative algebras

Keywords:

Leibniz algebra; cyclic Leibniz algebra; low-dimensional examples
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\textit{W. J. Cook} et al., Involve 12, No. 5, 839--853 (2019; Zbl 1477.17017)
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References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.