Verona

On a class of quasi-hereditary algebras arising from Reedy categories

Georgios Dalezios, University of Verona

Abstract

The natural numbers and the weakly monotone functions between them form a category, called the cosimplicial indexing category, which is fundamental in the theory of simplicial sets. A Reedy category is a certain generalization, heavily used in homotopy theory. In this talk, we focus on Reedy categories having finitely many objects (any truncation of the cosimplicial indexing category is an example). We introduce a class of finite dimensional associative algebras, which we call Reedy algebras, and provide two main results. The first is that Reedy algebras are quasi-hereditary; the latter class of algebras was introduced by Cline, Parshall and Scott and has been studied extensively in representation theory. The second main result characterizes Reedy algebras as those quasi-hereditary algebras admitting a so-called Cartan decomposition. The talk is based on joint work with J. Stovicek and on joint work with T. Conde and S. Koenig.