# Journal of Operator Theory

Volume 38, Issue 1, Summer 1997 pp. 3-18.

The structure of twisted convolution C*-algebras on abelian groups**Authors**: Detlev Poguntke

**Author institution:**Universität Bielefeld, Fakultät für Mathematik, Postfach 100 131, 33501 Bielefeld, GERMANY

**Summary:**Let $\mathcal G$ be a locally compact two step nilpotent group. Each unitary character $\lambda$ on the closure of the commutator subgroup defines in a canonical fashion a quotient $C*(\mathcal G)_\lambda$ of the group C*-algebra $C*(\mathcal G)$. Under a mild extra condition, which is e.g. satisfied if $\mathcal G$ is compactly generated, the structure of C*(\mathcal G)_\lambda is determined completely. This result is applied to connected Lie groups in order to obtain the structure of certain subquotients of the corresponding group C*-algebras.

**Keywords:**Two step nilpotent groups, Lie groups, group C*-algebras, non-commutative tori, stable isomorphy, cocycles, imprimitivity theorem.

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