Vershik, A. M. Strange factor representations of type II\(_1\) and pairs of dual dynamical systems. (English) Zbl 1059.46041 Mosc. Math. J. 3, No. 4, 1441-1457 (2003). Summary: Given a pair of dynamical systems, we construct a pair of commuting factors of type \(\text{II}_1\). This construction is a generalization of the classical von Neumann-Murray construction of factors as crossed products and of the groupoid construction. The suggested construction provides natural examples of factors with non-unity coupling constant. First examples of this kind, related to actions of abelian groups and to the theory of quantum tori, were given by Connes and Rieffel and by Faddeev; our generalization includes these examples as well as new examples of factorizations related to lattices in Lie groups, the infinite symmetric group, etc. Cited in 1 Document MSC: 46L10 General theory of von Neumann algebras 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 37A99 Ergodic theory 37B99 Topological dynamics Keywords:coupling constant; dynamical system; factor representation; Heisenberg group; pseudogroupoid; infinite symmetric group Citations:Zbl 0633.46069; Zbl 0836.47012 PDFBibTeX XMLCite \textit{A. M. Vershik}, Mosc. Math. J. 3, No. 4, 1441--1457 (2003; Zbl 1059.46041) Full Text: arXiv