zbMATH — the first resource for mathematics

Twisted crossed products of \(C^*\)-algebras. (English) Zbl 0757.46056
Let \(A\) be a \(C^*\) algebra and let \(\operatorname{Aut} A\) and \(UM(A)\) denote the automorphism group and the group of unitary elements of the multiplier algebra \(M(A)\) of \(A\). A twisted action of a locally compact group \(G\) on \(A\) consists of Borel maps \(\alpha: G\to\operatorname{Aut} A\) and \(u: G\times G\to UM(A)\) satisfying \[ \alpha_ s\alpha_ t=\text{Ad} u(s,t)\circ\alpha_{st}, \qquad \alpha_ r(u(s,t))u(r,st)=u(r,s)u(rs,t). \] In this paper the authors study the basic properties of the system \((A,G,\alpha,u)\).

46L55 Noncommutative dynamical systems
Full Text: DOI
[1] DOI: 10.1017/S0305004100061119 · Zbl 0526.46063
[2] DOI: 10.1090/S0002-9947-1970-0264418-8
[3] Zeller-Meier, J. Math. Pures Appl. 47 pp 101– (1968)
[4] Yoshida, Functional Analysis (1974)
[5] Reed, Functional Analysis (1972)
[6] Raeburn, Proc. Centre Math. Anal. Austral. Nat. Univ. 15 pp 214– (1987)
[7] Doran, Approximate Identities and Factorisation in Banach Modules 768 (1979) · Zbl 0418.46039
[8] DOI: 10.1512/iumj.1986.35.35029 · Zbl 0581.46054
[9] Pedersen, C*-algebras and their Automorphism Groups (1979)
[10] DOI: 10.1090/S0002-9947-1976-0414775-X
[11] DOI: 10.1007/BF01425550 · Zbl 0175.44601
[12] Hille, Functional Analysis and Semigroups (1957)
[13] DOI: 10.1007/BF02392308 · Zbl 0407.46053
[14] DOI: 10.1017/S0013091500003436 · Zbl 0674.46038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.