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

[摘要] 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) circle times 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. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] C*-algebra;Finite dimensional irreducible representation;Local multiplier algebra;Derivation