Lie algebra

English

Etymology

Named in honor of Sophus Lie (1842–1899), a Norwegian mathematician, in the 1930s by Hermann Weyl.

Pronunciation

• IPA^(key): /liː.ældʒɨbɹə/

Noun

Lie algebra (plural Lie algebras)

1. (mathematics) An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket.

Derived terms

• Lie bialgebra
• Lie coalgebra
• Lie superalgebra

Translations

algebraic structure

• Finnish: Lien algebra
• German: Lie-Algebra
• Japanese: リー代数 (rīdaisū)
• Russian: а́лгебра Ли f (álgebra Li)
• Serbo-Croatian:

  Roman: Liejeva algebra f