View source for Commutant

==English==

===Etymology===
From {{suffix|en|commute|ant}}.

===Pronunciation===
* {{audio|en|LL-Q1860 (eng)-Flame, not lame-commutant.wav|a=US}}

===Noun===
{{en-noun}}

# {{lb|en|algebra|logic}} The subset of all elements of a [[semigroup]] that [[commute]] with the elements of a given subset
#* {{quote-journal|en|date=September 27, 2008|author=John Earman|title=Superselection Rules for Philosophers|work=Erkenntnis|doi=10.1007/s10670-008-9124-z|volume=69|issue=3|url=
|passage=The basic mathematical entity to be used here in elucidating the different senses of superselection rules is a von Neumann algebra <math>{\mathfrak{M}},</math> a concrete C * -algebra 6 of bounded linear operators acting on a Hilbert space 7 <math>{\mathcal{H}}</math> that is closed in the weak topology 8 or, equivalently, 9 that has the property that <math>({\mathfrak{M}}^{\prime})^{\prime}:={\mathfrak{M}}^{\prime \prime }={\mathfrak{M}},</math> where “′” denotes the '''commutant'''.}}

====Derived terms====
{{col|en|bicommutant|commutant lifting theorem}}

====See also====
* {{pedia}}

==French==

===Participle===
{{head|fr|present participle}}

# {{present participle of|fr|commuter}}

==Latin==

===Verb===
{{head|la|verb form|head=commūtant}}

# {{inflection of|la|commūtō||3|p|pres|actv|indc}}