Lattice-ordered pregroups (l-pregroups) are exactly the involutive residuated lattices where addition and multiplication coincide. Among them, for every positive integer n, the n-periodic l-pregroup F_n(Z) of n-periodic order-preserving functions on the integers plays an important role in understanding distributive l-pregroups and also n-periodic ones. We give a finite axiomatization of the variety generated by F_n(Z). On the way we also obtain some more general results about periodic l-pregroups and we characterize the finitely subdirectly irreducibles of the variety generated by F_n(Z). Joint work with Nick Galatos.
Axiomatizing small varieties of periodic l-pregroups
Tue, Nov. 18 2:30pm (MATH 2…
Grad Algebra/Logic
Khizar Pasha (CU Boulder)
X
Continuation of last week's talk.
Bounded width CSPs, 2
Tue, Nov. 18 2:30pm (MATH 3…
Lie Theory
Mandi Schaeffer-Fry (DU)
X
The McKay Conjecture (now a theorem due to Cabanes--Späth) says that there is a bijection between irreducible characters of a finite group G with degree not divisible by p and the corresponding set for the normalizer of a Sylow p-subgroup. Several Galois refinements of this Conjecture exist, positing that the bijection should be compatible with fields of values. I'll discuss joint work with Lucas Ruhstorfer, in which we complete the proof of the original of these Galois refinements, proposed by Isaacs--Navarro in 2002. I'll also discuss several consequences, giving additional local-global properties in the character theory of finite groups.
Axiomatizing small varieties of periodic l-pregroups