Nonassociative rings and algebras Lie superalgebras and generalizations of Lie algebras Concept
Malcev algebra
Summary
A Malcev algebra is an anticommutative algebra that satisfies a weakened form of the Jacobi identity, the Malcev identity. Every Lie algebra is a Malcev algebra, and the commutator algebra of every alternative algebra is a Malcev algebra. Malcev algebras are to analytic Moufang loops what Lie algebras are to Lie groups. The purely imaginary octonions with the commutator bracket form a seven-dimensional simple Malcev algebra that is not a Lie algebra.
Further reading
About this page
| Tag | 9G3TWHYBH9 |
|---|---|
| URI | m2://9G3TWHYBH9 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 17D10 |
| Specializes | Anticommutative algebra |
| Same as | |
| Changed | 3 November 2026 |
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