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arXiv · 1503.03733

Invariant means on Boolean inverse monoids

Ganna Kudryavtseva·Mark V. Lawson·Daniel H. Lenz·Pedro Resende
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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.

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Ganna Kudryavtseva, Mark V. Lawson, Daniel H. Lenz, Pedro Resende. 2015-03-12. Invariant means on Boolean inverse monoids. https://arxiv.org/abs/1503.03733

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