Finite dimensional representations of classical crossed-product algebras
type: Item
instance of: scholarly article
title: Finite dimensional representations of classical crossed-product algebras
zbMATH Open document ID: 0632.46059
author: Igal Megory-Cohen
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 4028177
zbMATH Keywords: structure of finite dimensional representations
zbMATH Keywords: crossed-product algebra of a classical dynamical system
zbMATH Keywords: orbits
zbMATH Keywords: hyperbolic automorphism
MaRDI profile type: Publication
full work available at URL: pjm.1988.135.349
OpenAlex ID: W1977899044
DOI: 10.2140/PJM.1988.135.349
Recommended article: Q3784659
Recommended article: Representations of finite-dimensional Hopf algebras
Recommended article: FINITE DIMENSIONAL REPRESENTATIONS OF u-HOPF ALGEBRAS
Recommended article: Finite-dimensional representations of \(W\)-algebras
Recommended article: Hilbert space representations of cross product algebras
Recommended article: Finite-dimensional representations of quantum affine algebras
Recommended article: FINITE-DIMENSIONAL REPRESENTATIONS OF FREE PRODUCT C*-ALGEBRAS
Recommended article: Irreducible representations of crossed products
Recommended article: Q5447461
description: scientific article; zbMATH DE number 4028177