Lie algebra

/liː.ældʒɨbɹə/

noun

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.

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Meanings

nounLie algebra (plural Lie algebras)

plural Lie algebras

  1. mathematicsAn 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.

Origin

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

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Translations

Bulgarian алгебра на Ли
  • алгебра на Ли (algebra na Li)algebraic structure
Finnish Lien algebra
  • Lien algebraalgebraic structure
German Lie-Algebra
  • Lie-Algebraalgebraic structure
Japanese リー代数
  • リー代数 (rīdaisū)algebraic structure
Polish algebra Liego
  • algebra Liegoalgebraic structure
Russian а́лгебра Ли
  • а́лгебра Ли (álgebra Li)algebraic structure
Cite this entry
APA

Lie algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Lie%20algebra

MLA

“Lie algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Lie%20algebra. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Lie algebra,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Lie%20algebra.

Source: Lie algebra on Wiktionary, CC BY-SA 4.0.