BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Itamar Stein (Ashdod) DTSTART:20201015T090000Z DTEND:20201015T100000Z DTSTAMP:20260419T055715Z UID:CRMDS/21 DESCRIPTION:Title: R epresentation theory of the monoid of all partial functions on a set and o ther Ehresmann semigroups\nby Itamar Stein (Ashdod) as part of Western Sydney University Abend Seminars\n\n\nAbstract\nGiven a finite semigroup S\, we can study its linear representations (for this talk - over the fiel d of complex numbers). Semigroups with natural combinatorial structure are clearly of major interest. An important example of such semigroup is the monoid of all partial functions on an n element set\, denoted PT_n. A desc ription of its simple modules by induced left Schützenberger modules was obtained in the fifties by Munn and Ponizovskii as part of a more general work on the representation theory of finite semigroups. Unlike group algeb ras\, semigroup algebras are seldom semisimple and therefore have (none-se misimple) projective modules. We give a description of the indecomposable projective modules of PT_n which is similar in spirit to the Munn-Ponizovs kii construction of the simple modules. Moreover\, we generalize both resu lts and describe the simple and the indecomposable projective modules of a certain class of Ehresmann semigroups\, with the case of PT_n being a nat ural example. This is a joint work with Stuart Margolis.\n LOCATION:https://researchseminars.org/talk/CRMDS/21/ END:VEVENT END:VCALENDAR