Algebra Seminar talk

2022-08-17 (Wed! 13:00!)
Leon Renkin
All Centralizing Monoids on a Three-Element Set


For a set of operations F, the centralizer is defined as the set of functions which commute with every operation in F. The unary part of a centralizer is called a centralizing monoid. For a universal algebra, the unary part of the centralizer of its set of fundamental operations is precisely the endomorphism monoid of the algebra. The set of operations of the algebra is called a witness for this monoid.

In this seminar talk, I will give an introduction to formal concept analysis as a means for manipulating Galois connections, and I will explain the basics of centralizing monoids on finite sets. Furthermore, I will present a strategy to determine all 192 centralizing monoids and corresponding witnesses on a three-element set.