BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jonathan Warne (UEA) DTSTART:20241022T130000Z DTEND:20241022T140000Z DTSTAMP:20260421T153817Z UID:UEAPS/39 DESCRIPTION:Title: F actorisations of finitely presented special inverse monoids\nby Jonath an Warne (UEA) as part of ANTLR seminar\n\nLecture held in JSC 2.02.\n\nAb stract\nInverse monoids are a kind of algebraic object which model partial bijections in the same way that groups model bijections and semigroups mo del transformations generally. A special inverse monoid is one defined by a set of relations of the form $r_i = 1$. We can factorise these $r_i$ int o component words\, for instance $xyxzxy =1$ may be written $(xy)(xz)(xy) =1$. In particular\, every special inverse monoid presentation has a uniqu e factorisation of its relators into minimal invertible pieces.\n\nIn 2001 Ivanov\, Margolis and Meakin produced a paper which included amongst othe rs two important results. That the special inverse monoid's group of units is generated by the minimal invertible pieces and that we can decide the word problem of an E-unitary special inverse monoid by deciding the word a nd prefix membership problems of its maximal group image. Both allow us to better understand an inverse monoid by studying corresponding groups.\n\n In this talk we will use these results to discuss the effects of the minim al invertible pieces of a special inverse monoid's relators having certain combinatorial properties on a number of decision problems\, extending res ults by Dolinka and Gray.\n LOCATION:https://researchseminars.org/talk/UEAPS/39/ END:VEVENT END:VCALENDAR