Derivatives for equational theories and a special case of Taylor's conjecture
 
 
Description: 

The theory of Maltsev conditions has provided many useful characterizations of properties of varieties, like permutability or modularity of congruence lattices, by the satisfaction of certain identities. The notion of "derivative" for a  an equational theory (or, equivalently, for a variety, by Birkhoff's celebrated theorem) was recently introduced by Dent, Kearnes and Szendrei. In a seminal paper, these authors showed how properties of the derivative are closely related to congruence modularity, and how the derivative can be used to obtain easy proofs of many classic results. Taylor's modularity conjecture, which remains open, states that one can not obtain a congruence modular variety as a join (in the interpretability lattice) of two non modular varieties. In this talk, I will explain the relevant notions and show how, using the notion of derivative, we were able to settle in the affirmative a special case of Taylor's conjecture.

(joint work with Wolfram Bentz)

Date:  2014-01-09
Start Time:   15:30
Speaker:  Luís Sequeira (CAUL, Univ. Lisboa)
Institution:  CAUL, Universidade de Lisboa
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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