Nonassociative rings and algebras Lie superalgebras and generalizations of Lie algebras Concept
Leibniz algebra
Summary
A Leibniz algebra is a nonassociative algebra in which multiplication by a fixed element is a derivation of the product. Every Lie algebra is a Leibniz algebra, and a Leibniz algebra in which every square vanishes is a Lie algebra. So Leibniz algebras are "Lie algebras without antisymmetry". They were studied by Loday, who introduced a Leibniz homology theory for them.
Further reading
About this page
| Tag | FGM1ZM3KKN |
|---|---|
| URI | m2://FGM1ZM3KKN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 17A32 |
| Specializes | Nonassociative algebra |
| Same as | |
| Changed | 3 November 2026 |
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