Ross Willard (University of Waterloo), Characterizing [alpha,beta]=0 using Kiss terms

Tue, 1 February 2022, 1 pm MST

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.

[slides] [preprint] [video]