Michael Kompatscher – Failure of local-to-global

University of Oxford

For several Maltsev conditions (e.g. the existence of a Maltsev term, majority term, or cyclic term of a fixed arity) it suffices to check if they hold 'locally' (i.e. restricted to every tuple) in order to determine if they are satisfied 'globally' in a finite idempotent algebra. Using this 'local-to-global' property is one of the few known methods to show the tractability of checking a fixed Maltsev condition.

In this talk, I would like to discuss the local-to-global approach for terms, whose variables are invariant under permutations from a given permutation group $G$ . In several cases, including symmetric terms of arity $n>2$ (so $G = S_n$ is the symmetric group) the local-to-global approach fails.

This is joint work with Alexandr Kazda.