Some subsemigroups of extensions of C^*-algebras

Abstract

In this paper we investigate the structure of the subsemigroup generated by the inner automorphisms in \mathbf{Ext}(\mathscr{L}, \bm{K}). As an application, we give a new point of view to the example of J. Plastiras, which are two C^*-algebras \mathfrak{U} and \mathfrak{B} satisfying \mathfrak{U}¬≅ \mathfrak{B} and \bm{M}₂otimes \mathfrak{U}≅ \bm{M}₂otimes \mathfrak{B}.