Characterizing [alpha,beta]=0 using Kiss terms

Abstract: 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.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.