Lie algebra

In mathematics, a Lie algebra (/liː/, not /laɪ/) is a vector space together with a non-associative multiplication called "Lie bracket" . When an algebraic product is defined on the space, the Lie bracket is the commutator .

Lie algebras were introduced to study the concept of infinitesimal transformations. Hermann Weyl introduced the term "Lie algebra" (after Sophus Lie) in the 1930s. In older texts, the name "infinitesimal group" is used.