caa a22 4500 388046880 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.1017/S1446788700039227 doi S1446788700039227 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700039227 Dual symmetric inverse monoids and representation theory [Elektronische Daten] There is a substantial theory (modelled on permutation representations of groups) of representations of an inverse semigroup S in a symmetric inverse monoid Ix, that is, a monoid of partial one-to-one selfmaps of a set X. The present paper describes the structure of a categorical dual Ix* 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 Ix and Ix*, 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. Copyright © Australian Mathematical Society 1998 primary 20M18 nationallicence secondary 20M30 nationallicence Fitzgerald D. G. School of Mathematics and Physics University of Tasmania PO BOx 1214 Launceston, Australia 7250 e-mail: D.FitzGerald@utas.edu.au Leech Jonathan Department of mathematics Westmont College 955 La Paz Road, Santa Barbara California 93108-1099 USA e-mail: leech@westmont.edu Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 345-367 1446-7887 64:3<345 1998 64 JAZ https://doi.org/10.1017/S1446788700039227 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700039227 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fitzgerald D. G. School of Mathematics and Physics University of Tasmania PO BOx 1214 Launceston, Australia 7250 e-mail: D.FitzGerald@utas.edu.au NATIONALLICENCE 700 1- Leech Jonathan Department of mathematics Westmont College 955 La Paz Road, Santa Barbara California 93108-1099 USA e-mail: leech@westmont.edu NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 345-367 1446-7887 64:3<345 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge