Seminari del Dipartimento di Matematica

Seminario del 2024

Homological algebra for pro-Lie Polish groups

nell'ambito della serie: LOGIC, CATEGORIES, AND APPLICATIONS SEMINAR

algebra e geometria

logica

Enriching traditional algebraic structures such as abelian groups with a topology runs into some issues from the Homological Algebra point of view, as the categories thus obtained are not, in general, classical abelian categories, but instead only satisfy the weaker notion of being quasi-abelian. The additional homological work required to deal with topological abelian groups has traditionally been carried out for Locally Compact Groups by Moskowitz with extensive use of the Pontryagin duality. However, this work has shown that Locally Compact Groups do not satisfy some useful homological properties. In this talk I will introduce the category of pro-Lie Polish groups, a recently proposed generalization of Polish Locally Compact Groups, and discuss why they are better suited as an object of study of Homological Algebra.