# Algebra Seminar talk

2018-10-19 (10:15)

Felix **Schiffer***Equivalence of loop conditions*

Abstract:

In a given algebra (or variety) certain identities, so called Maltsev
conditions, do or do not hold. A special case of them, given only by a single
identity, are called loop conditions. A loop condition implies a second one, if
in every variety in which the first one holds also the second one does. An
elegant way to show these implications uses the special form of these
identities (which can be interpreted as a digraph) and digraph homomorphisms.

In this talk I will present some results from the paper "Loop conditions" by Miroslav Olšák in which he used the above mentioned strategy to show that there are exactly three equivalent classes of loop conditions given by undirected graphs.