Dual Symmetric Inverse Monoids and Representation Theory
FitzGerald, DG and Leech, J (1998) Dual Symmetric Inverse Monoids and Representation Theory. Journal of the Australian Mathematical Society, Series A, 64 (3). pp. 345367. ISSN 02636115  PDF  Full text restricted  Requires a PDF viewer 158Kb  
Official URL: http://www.austms.org.au/Publ/Jamsa/V64P3/pdf/e07.pdf AbstractThere is a substantial theory (modelled on permutation representations of groups) of representations of an
inverse semigroup S in a symmetric inverse monoid I_X , that is, a monoid of partial onetoone selfmaps
of a set X. The present paper describes the structure of a categorical dual I*_X to the symmetric inverse
monoid and discusses representations of an inverse semigroup in this dual symmetric inverse monoid. It
is shown how a representation of S by (full) selfmaps of a set X leads to dual pairs of representations
in I_X and I*_X, and how a number of known representations arise as one or the other of these pairs.
Conditions on S are described which ensure that representations of S preserve such infima or suprema as
exist in the natural order of S. The categorical treatment allows the construction, from standard functors,
of representations of S in certain other inverse algebras (that is, inverse monoids in which all finite infima
exist). The paper concludes by distinguishing two subclasses of inverse algebras on the basis of their
embedding properties. Item Type:  Article 

Keywords:  dual symmetric inverse monoid, representations of inverse semigroups 

ID Code:  1911 

Deposited By:  Dr D. G. FitzGerald 

Deposited On:  17 Sep 2007 

Last Modified:  18 Jul 2008 20:09 

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