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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 \((A,G,\alpha,u)\).

MSC:
46L55 Noncommutative dynamical systems
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[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
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