2011/11/14 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · Medicine · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Neurological disorders and treatments #math.DS #math.OA #msc:46L35
paper · pdf · doi:10.48550/arxiv.1111.3091
48 pages
arxiv created 2011/11/14 · arxiv updated 2011/11/15
A C^*-textile dynamical system (\cal A, ρ,η,Σρ,Ση, κ) connsists of a unital C^*-algebra \cal A, two families of endomorphisms ραα∈ Σρ and ηaa ∈ Ση of \cal A and certain commutation relations κ among them. It yields a two-dimensional subshift and multi structure of Hilbert C^*-bimodules, which we call a Hilbert C^*-quad module. We introduce a C^*-algebra from the Hilbert C^*-quad module as a two-dimensional analogue of Pimsner's construction of C^*-algebras from Hilbert C^*-bimodules. We study the C^*-algebras defined by the Hilbert C^*-quad modules and prove that they have universal properties subject to certain operator relations. We also present its examples arising from commuting matrices.