Commutant

From Free net encyclopedia

In algebra, the commutant A of a subset S of an algebra over a field K is the subset S′ of elements of A commuting with every element of S. In other words,

<math>S'=\{x\in A: sx=xs\ \mbox{for}\ \mbox{every}\ s\in S\}.</math>

S′ forms a subalgebra. This is analogous to the concept of a centralizer in group theory.

See also

• Bicommutant
• von Neumann bicommutant theorem