# Tag Info

• 42.4k
Accepted

### Maximal ideals of ultraproducts of full matrix algebras

I think Nik Weaver is right that the ideal mentioned is the unique maximal ideal. This simultaneously answers both questions (since the quotient is clearly infinite dimensional). Let $\tau$ be the ...
• 2,679
Accepted

### On equation $e^{xy-yx}=e^xe^ye^{-x}e^{-y}$ in $C^*$ algebras

Yes: A $C^*$-algebra satisfies the identity $e^{[xy-yx]}=e^xe^ye^{-x}e^{-y}$ iff it is commutative. This follows from two independent facts (I write $[x,y]=xy-yx$) 1) A (real/complex) unital ...
• 61k
Accepted

### Amenable action intuition

It is impossible to understand the motivation behind the definition of an amenable action without first understanding the definition of amenable groups, so let me first talk about groups (for ...
• 16.8k

### Which $\ast$-algebras are $C^\ast$-algebras?

Given an algebra $A$, one can ask whether it has a unit. If one exists, one then shows it is unique: $1_A = 1_A1_A' = 1_A'$. Thus being unital is a property of an algebra and not extra structure. ...
• 5,335