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 YG 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 YG such that the global group action of G on YG is continuous and the injection Y into YG is an open dense equivariant embedding.
Authors:Karin Cvetko-Vah, Damjana Kokol Bukovšek, Tomaž Košir and Ganna Kudryavtseva
We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part of the symmetric inverse semigroup is 2n−p+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.
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.
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.