Finite dimensional representations of classical crossed-product algebras
The paper describes the structure of finite dimensional representations of \(B_ T\), the crossed-product algebra of a classical dynamical system \((\alpha _ t,{\mathbb{Z}},C(X))\) where T is a homeomorphism on a compact space X. The results are used to describe the topology of \(\Pr im_ n(B_ T)\) and to partially classify the hyperbolic crossed-product algebras over the torus. One of the main results is that the number of orbits of any fixed length with respect to T is an invariant of \(B_ t\). A consequence of that is that the entropy of T is an invariant of \(B_ T\), for T a hyperbolic automorphism on the m-torus.
structure of finite dimensional representations
crossed-product algebra of a classical dynamical system
scientific article; zbMATH DE number 4028177
scientific article