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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 383
Actions of finite abelian groups on abelian C*-algebras Z: Second cohomology and description by C*-extensions F supset Z H. Baumgärtel
The paper discusses the second cohomology $H^{2}({cal Z}, Gamma)$ w.r.t. a modified cocycle equation, given by a finite abelian automorphism group $Gammasubset mbox{aut},{cal Z}$. A complete description of $H^{2}$ is given for the cyclic group $Gamma cong Z_{N}$. The discussion and solution of the case $Gammacong Z_{2} imes Z_{2}$ points to the difficulty to figure out a "composition principle" for direct products. The connection with the "outer" description of $H^{2}({cal Z}, Gamma)$ by extensions ${cal F}supset {cal Z}$ is pointed out
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