A Lie algebra is a mathematical concept used to study the structure of certain kinds of algebraic objects, such as Lie groups. It is a vector space with a special kind of bilinear multiplication, called the Lie bracket, that satisfies certain axioms. Synonyms for Lie algebra include Lie ring, anti-commutative algebra, and non-associative algebra. These terms are all related to the structural properties of Lie algebras and how they differ from other types of algebras. The Lie ring, for example, is a type of non-associative algebra that does not necessarily satisfy the more stringent requirements of a Lie algebra. The term anti-commutative algebra emphasizes the skew-symmetry of the Lie bracket.