Inverse semigroups acting on graphs
Inverse semigroups acting on graphs
There has been much work done recently on the action of semigroups on sets with some important applications to, for example, the theory and structure of semigroup amalgams. It seems natural to consider the actions of semigroups on sets 'with structure' and in particular on graphs and trees. The theory of group actions has proved a powerful tool in combinatorial group theory and it is reasonable to expect that useful techniques in semigroup theory may be obtained by trying to 'port' the Bass-Serre theory to a semigroup context.
Given the importance of transitivity in the group case, we believe that this can only reasonably be achieved by restricting our attention to the class of inverse semigroups. However, it very soon becomes apparent that there are some fundamental differences with inverse semigroup actions and even such basic notions such as free actions have to be treated carefully. We make a start on this topic in this paper by first of all recasting some of Schein's work on representations by partial homomorphisms in terms of actions and then trying to 'mimic' some of the basic ideas from the group theory case. We hope to expand on this in a future paper.
9812389172
212-239
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
2004
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Renshaw, James
(2004)
Inverse semigroups acting on graphs.
Araújo, Isabel M., Branco, Mário J. J., Fernandes, Vítor H. and Gomes, Gracinda M. S.
(eds.)
In Semigroups and Languages.
World Scientific.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
There has been much work done recently on the action of semigroups on sets with some important applications to, for example, the theory and structure of semigroup amalgams. It seems natural to consider the actions of semigroups on sets 'with structure' and in particular on graphs and trees. The theory of group actions has proved a powerful tool in combinatorial group theory and it is reasonable to expect that useful techniques in semigroup theory may be obtained by trying to 'port' the Bass-Serre theory to a semigroup context.
Given the importance of transitivity in the group case, we believe that this can only reasonably be achieved by restricting our attention to the class of inverse semigroups. However, it very soon becomes apparent that there are some fundamental differences with inverse semigroup actions and even such basic notions such as free actions have to be treated carefully. We make a start on this topic in this paper by first of all recasting some of Schein's work on representations by partial homomorphisms in terms of actions and then trying to 'mimic' some of the basic ideas from the group theory case. We hope to expand on this in a future paper.
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Published date: 2004
Venue - Dates:
Proceedings of the Workshop: Semigroups and Languages 2002, Lisbon, Portugal, 2002-11-27 - 2002-11-29
Identifiers
Local EPrints ID: 29862
URI: http://eprints.soton.ac.uk/id/eprint/29862
ISBN: 9812389172
PURE UUID: ecce9060-e64f-4321-bc7e-aaf9d588fab6
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Date deposited: 15 May 2006
Last modified: 12 Dec 2021 02:39
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Contributors
Editor:
Isabel M. Araújo
Editor:
Mário J. J. Branco
Editor:
Vítor H. Fernandes
Editor:
Gracinda M. S. Gomes
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