Phrase guide

Lie algebra

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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  • /liː.ældʒɨbɹə/

1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

7 source translations are retained for this English entry.

  • Bulgarian: алгебра на Ли (algebra na Li) — algebraic structure
  • Finnish: Lien algebra — algebraic structure
  • German: Lie-Algebra — algebraic structure
  • Japanese: リー代数 (rīdaisū) — algebraic structure
  • Polish: algebra Liego — algebraic structure
  • Russian: а́лгебра Ли (álgebra Li) — algebraic structure
  • Serbo-Croatian: Liejeva algebra — algebraic structure