Semigroups of local homeomorphisms and interaction groups
算子代数
2010-03-16 v2 动力系统
摘要
Given a semigroup of local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the first named author. Under suitable hypotheses we may also define a transformation groupoid whose C*-algebra turns out to be isomorphic to the crossed product algebra for the interaction group. Several examples are considered, including one which gives rise to a slightly different construction and should be interpreted as being the C*-algebra of a certain polymorphism.
引用
@article{arxiv.math/0608589,
title = {Semigroups of local homeomorphisms and interaction groups},
author = {Ruy Exel and Jean Renault},
journal= {arXiv preprint arXiv:math/0608589},
year = {2010}
}
备注
35 pages, no figures. Section 14 added to include an example of commuting endomorphisms not admiting a non-zero coherent cocycle