commutator

For $A$ a ring or associative algebra, the **commutator** of two elements $x,y \in A$ is the element

$[x,y] \coloneqq x y - y x
\,.$

For $G$ a group, the **group commutator** of two elements $a,b \in G$ is the element

$[a,b] \coloneqq a^{-1} b^{-1} a b
\,.$

- For $A$ an associative algebra, the underlying vector space of $A$ equipped with the commutator bracket is a Lie algebra $(A,[-,-])$.

Revised on November 19, 2017 15:20:31
by Urs Schreiber
(94.220.49.59)