Associativity and the co-smash product

Description:  The aim of this talk is to sketch some ideas in joint work-in-progress with Ülo Reimaa and Corentin Vienne. The original question we set out to answer was to characterise when the objects in a variety of algebras over a field K have a multiplication that is associative. What we found is a categorical description of the variety of commutative associative algebras over K amongst all so-called operadic varieties over K, where a set of multilinear identities suffices to describe the algebras in the variety. As it turns out, the variety of commutative associative algebras over K is the only operadic variety whose co-smash products are not just symmetric, but also associative in the sense of Carboni and Janelidze. Date:  2022-05-24 Start Time:   15:00 Speaker:  Tim Van der Linden (Université Catholique de Louvain, Belgium) Institution:  Université Catholique de Louvain Place:  ZOOM Research Groups: -Algebra, Logic and Topology See more:   <Main>