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[NOVA Math] Seminar of Algebra and Logic

09-01-2025

The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Algebra and Logic with the title: “Transformation representations of diagram monoids”. James East (Western Sydney University) is the speaker.

                                      

Abstract: Cayley's Theorem states that any finite monoid can be faithfully represented as a semigroup of transformations (self-maps) of a finite set. The minimum size of such a set is the (minimum transformation) degree of the monoid.
      We obtain formulae for the degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley-Lieb and Motzkin monoids. For example, the partition monoid
 Pn has degree 1 + ( B(+ 2) - B(n + 1) + B(n) ) / 2 for n ≥ 2, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections.

                           

This is joint work with Reinis Cirpons and James Mitchell, both at Univ St Andrews.

                              

Monday, January 13, 11h00-12h00.

Zoom link: https://videoconf-colibri.zoom.us/j/92565611443?pwd=diOblm3Pu1aC5vYRMoN1...