3
$\begingroup$

Cunz and Li defined defined C*-algebras for arbitrary rings with of course some condition. One can look at their article (http://arxiv.org/abs/0905.4861). My question: is the construction functorial? If not, for what kind of morphism of C*-algebras/rings will it work?

For group case I know: one has to consider morphism between C*-algebras $A$ to $B$ as essential *-homomorphism from $A$ to $\mathfrak{M}(B)$. Where $\mathfrak{M}(X)$ is the multiplier algebra of $X$.

$\endgroup$
2
  • $\begingroup$ If you mean the full ring C*-algebra, it is functorial with respect to ring homomorphisms preserving regular elements (and the chosen algebra on the subsets): This follows from the universal property. $\endgroup$ Jan 22, 2013 at 9:54
  • $\begingroup$ What is your morphism between C*-algebras? $\endgroup$
    – Sayan
    Jan 22, 2013 at 17:49

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.