We investigate the semilattices of Mal'cev blocks ("SMB algebras"), a quasivariety of Taylor algebras invented by R. McKenzie and the speaker in 2009. The Constraint Satisfaction Problem over SMB algebras was proved to be tractable by A. Bulatov in 2017, and he used this case as a template for his proof of the Dichotomy Conjecture. In Bulatov's terminology of edge-colored graphs of algebras, SMB algebras are the prime example of as-connected algebras. Any simplification of the tractability proof for SMB algebras gives hope that one can, using Bulatov's theory of edge colored graphs of algebras, generalize to a simplification of the proof of the Dichotomy Theorem, motivating our investigation.
We were trying to prove D. Zhuk's reduction of "irreducible instances", which are consistent enough, to binary absorbing subuniverses ("Zhuk's Reduction Theorem") for the case of SMB algebras. We prove two results: One is a special case of Zhuk's Reduction Theorem, but assuming only 1-consistency, i.e. when all constraint relations are subdirect subuniverses of the product. The second result states that Zhuk irreducible instances, which are also Maroti reduced and consistent enough, must have a solution.
Constraint Satisfaction Problem over semilattices of Mal'cev blocks (joint work with A. Prokic)
May. 06, 2021 4pm (Zoom (vir…
Rep Theory
David Ridout (University of Melbourne)
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Minimal models are simple vertex operator algebras (VOAs) for which the structure of the associated universal VOA is somehow maximally degenerate. Some minimal models are rational and -cofinite, eg those for Virasoro or , and some are not. I will look at some examples which are not, specifically the admissible-level affine minimal models associated with . The novelty here is the fact that the rank of the associated algebra is not .