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Abstract  

J. Kellendonk and M. V. Lawson established that each partial action of a group G on a set Y can be extended to a global action of G on a set Y G containing a copy of Y. In this paper we classify transitive partial group actions. When G is a topological group acting on a topological space Y partially and transitively we give a condition for having a Hausdorff topology on Y G such that the global group action of G on Y G is continuous and the injection Y into Y G is an open dense equivariant embedding.

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Authors: Karin Cvetko-Vah, Damjana Kokol Bukovšek, Tomaž Košir and Ganna Kudryavtseva

Abstract

We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part of the symmetric inverse semigroup is 2np+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.

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Authors: Nassraddin Ghroda and Victoria Gould

Abstract  

We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semigroups (a step that has previously proved to be awkward). We also put some earlier work of Gantos into a wider and clearer context, and pave the way for further progress.

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Abstract  

We characterise the maximal proper closed inverse submonoids of the polycyclic inverse monoids, also known as Cuntz inverse semigroups, and so determine all their primitive partial permutation representations. We relate our results to the work of Kawamura on certain kinds of representations of the Cuntz C*-algebras and to the branching function systems of Bratteli and Jorgensen.

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