Doplicher, Sergio; Roberts, John E. Endomorphisms of \(C^*\)-algebras, cross products and duality for compact groups. (English) Zbl 0702.46044 Ann. Math. (2) 130, No. 1, 75-119 (1989). Summary: We define a new kind of cross product of a \(C^*\)-algebra by semigroups of endomorphisms with properties related to permutation symmetry and the existence of conjugates. A compact group is then defined intrinsically by its dual action on the cross product. This construction yields a characterization of abstract compact group duals which is out of reach of the Tannaka-Krejn duality theory and is independent of that theory. It thereby solves the problem of proving the existence of a compact global gauge group in particle physics given only the local observables. Cited in 4 ReviewsCited in 62 Documents MSC: 46L55 Noncommutative dynamical systems Keywords:cross product of a \(C^ *\)-algebra by semigroups of endomorphisms; permutation symmetry; existence of conjugates; dual action; abstract compact group duals PDFBibTeX XMLCite \textit{S. Doplicher} and \textit{J. E. Roberts}, Ann. Math. (2) 130, No. 1, 75--119 (1989; Zbl 0702.46044) Full Text: DOI