Many years ago, Kiss proved that the commutator relation [alpha,beta]=0 can be characterized in congruence modular varieties by a simple condition involving a certain kind of 4-ary term, which is now called a Kiss term. Seven years ago, Kearnes, Szendrei and I claimed to extend this characterization to varieties having a difference term, and we used this at a key step in proving our finite basis theorem for finite algebras in varieties having a difference term and having a finite residual bound. It was recently brought to our attention that the published proof of our extension of Kiss’s result has a significant gap, bringing into question the validity of our finite basis theorem. In this talk I will sketch a new (correct) proof of this extension. This is joint work with Keith Kearnes and Agnes Szendrei.
Characterizing [alpha,beta]=0 using Kiss terms
Feb. 01, 2022 3pm (MATH 350)
Topology
Juan Moreno (CU Boulder)
X
This meeting is to kick-off a learning seminar on modular tensor categories (MTCs). The meeting will consist of a short overview of the topic after which participants will have the opportunity to sign up for talks.
MTCs, and more generally fusion categories, were designed to model the physics of anyon systems which offer a potential framework for quantum computation. Anyons are particles which arise as excitations in (2+1)D topological phases of matter. Such phases (or at least some subclass of them) are believed to have a low-energy description of a (2+1)D topological quantum field theory (TQFT). The goal for this seminar is to study MTCs and their relationship with TQFTs. While their motivation is primarily in the realm of physics, these objects are interesting as stand-alone mathematical objects: (2+1)D TQFTs give rise to 3-manifold and knot/link invariants, and many important examples of MTCs come from representation theory and the theory of quantum groups.