In mathematics, a Lie algebra (, not ) is a vector space together with a non-associative multiplication called "Lie bracket" . It was 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.

In mathematics, a Lie-* algebra is a D-module with a Lie* bracket. They were introduced by , and are similar to the conformal algebras discussed by and to vertex Lie algebras.