Invariant means on Boolean inverse monoids
Category Theory
2015-03-13 v1
Abstract
The classical theory of invariant means, which plays an important role in the theory of paradoxical decompositions, is based upon what are usually termed `pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise to etale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Our main theorem is a characterization of when a Boolean inverse monoid admits an invariant mean. This generalizes the classical Tarski alternative proved, for example, by de la Harpe and Skandalis, but using different methods.
Cite
@article{arxiv.1503.03733,
title = {Invariant means on Boolean inverse monoids},
author = {Ganna Kudryavtseva and Mark V. Lawson and Daniel H. Lenz and Pedro Resende},
journal= {arXiv preprint arXiv:1503.03733},
year = {2015}
}