Structure of the group of automorphisms of C${}^{\ast }$-algebras

Abstract

We obtain a kind of structure theorem for the automorphism group $\mathrm{Aut}\mathcal{A}$ of a unital C${}^{\ast }$-algebra $\mathcal{A}$. According to it, $\mathrm{Aut}\mathcal{A}$ can be regarded as a subgroup of the semi-direct product of direct product group consisting of some family of projective unitary groups and some permutation group on the spectrum of $\mathcal{A}$.

11 pages, LaTeX