Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 385

Group actions on C*-algebras and their description by Hilbert C*-extensions

H. Baumgärtel

Automorphism groups $Gamma$ of $C^{ast}$-algebras ${cal A}$ are considered, where $gamma_{1}circ,gamma_{2}$ and $gamma_{2}circ,gamma_{1}$ are unitarily equivalent for all $gamma_{1},gamma_{2} in Gamma$. The paper discusses the problem of the existence of Hilbert $C^{ast}$-extensions ${{cal F},alpha({cal G})}$ of ${{cal A},Gamma}$, in particular its cohomological aspect.

the center ${cal Z}subseteq {cal A}$ of ${cal A}$ is trivial, ${cal Z}=Bbb{C}EINS$, then then this problem is a special case (the abelian or automorphism case) of the Doplicher-Roberts duality theory for compact groups (see [1, 2, 3, 4]). Special cases with ${cal Z}supset Bbb{C}EINS$ are presented, where the existence of Hilbert-$C^{ast}$-extensions can be proved.

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