# commutant

## English

### Noun

commutant (plural commutants)

1. (algebra, logic) The subset of all elements of a semigroup that commute with the elements of a given subset
• 2008 September 27, John Earman, “Superselection Rules for Philosophers”, in Erkenntnis, volume 69, number 3, DOI:10.1007/s10670-008-9124-z:
The basic mathematical entity to be used here in elucidating the different senses of superselection rules is a von Neumann algebra ${\displaystyle {\mathfrak {M}},}$ a concrete C * -algebra 6 of bounded linear operators acting on a Hilbert space 7 ${\displaystyle {\mathcal {H}}}$ that is closed in the weak topology 8 or, equivalently, 9 that has the property that ${\displaystyle ({\mathfrak {M}}^{\prime })^{\prime }:={\mathfrak {M}}^{\prime \prime }={\mathfrak {M}},}$ where “′” denotes the commutant.

commutant

commūtant