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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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##### References:
 [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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