Abstract
As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoidsof a polycyclic monoid and classified them up to conjugacy. We show that Lawson's description can be extended to closed inverse subsemigroups of graph inverse semigroups. We then apply B. Schein's theory of cosets in inverse semigroups to the closed inverse subsemigroups of graph inverse semigroups: we give necessary and sufficient conditions for a closed inverse subsemigroup of a graph inverse semigroup to have finite index, and determine the value of the index when it is finite.
Original language  English 

Pages (fromto)  46674678 
Number of pages  12 
Journal  Communications in Algebra 
Volume  45 
Issue number  11 
Early online date  6 Jan 2017 
DOIs  
Publication status  Published  2 Nov 2017 
Keywords
 Inverse semigroup
 coset
 graph
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Nick Gilbert
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)