Baaj, Saad; Skandalis, Georges Pentagonal transformations. (Transformations pentagonales.) (French. Abridged English version) Zbl 1040.37500 C. R. Acad. Sci., Paris, Sér. I, Math. 327, No. 7, 623-628 (1998). Summary: We prove that every bimeasurable transformation \(\upsilon : X \times X \to X \times X\), where \(X\) is a measured space satisfying the pentagon identity \(\upsilon_{23} \circ\upsilon_{13}\circ\upsilon_{12} = \upsilon_{12}\circ \upsilon_{23}\) (and sufficiently regular) comes from a matched pair of locally compact groups, i.e., a locally compact group \(G\) and two closed subgroups, \(G_1\) and \(G_2\) such that the map \((g_1, g_2) \mapsto g_1g_2\) is a homeomorphism from \(G_1 \times G_2\) onto a dense open subset of \(G\). Cited in 8 Documents MSC: 37A05 Dynamical aspects of measure-preserving transformations 22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations 46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory 28D05 Measure-preserving transformations PDFBibTeX XMLCite \textit{S. Baaj} and \textit{G. Skandalis}, C. R. Acad. Sci., Paris, Sér. I, Math. 327, No. 7, 623--628 (1998; Zbl 1040.37500) Full Text: DOI