Math 2.0

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

  1. Web https://en.wikipedia.org/wiki/Malcev_algebra
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Kindconcept
WritingW0 stub
MSC17D10
SpecializesAnticommutative algebra
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Changed3 November 2026

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