Naslov
The local multiplier algebra of a C*-algebra with finite dimensional irreducible representations

Autori
Gogić, Ilja

Izvornik
Journal of mathematical analysis and applications (0022-247X) 408 (2013), 2; 789-794

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
C*-algebra ; finite dimensional irreducible representation ; local multiplier algebra ; derivation

Sažetak
We describe, up to isomorphism, the local multiplier algebra $M_{; ; ; loc}; ; ; (A)$ of a $C^*$-algebra $A$ which admits only finite dimensional irreducible representations: $M_{; ; ; loc}; ; ; (A)$ in this case is a finite or countable direct product of $C^*$-algebras of the form $C(X_n)\otimes M_n$, where each space $X_n$ is Stonean. In particular, $M_{; ; ; loc}; ; ; (A)$ is an $AW^*$-algebra of type I, so it admits only inner derivations and it coincides with the injective envelope $I(A)$ of $A$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA