An upper bound for the finitistic dimension of an EI category algebra

TL;DR

This paper establishes an upper bound for the finitistic dimension of EI category algebras, which combine properties of posets and finite groups, using a construction attributed to Lueck.

Contribution

It provides a novel upper bound for the finitistic dimension of EI category algebras, enhancing understanding of their homological properties.

Findings

Derived an explicit upper bound for the finitistic dimension

Connected algebraic structures of EI categories to known algebra classes

Applied Lueck's construction to this specific algebra class

Abstract

EI categories can be thought of as amalgams of finite posets and finite groups and therefore the associated algebras are built up from incidence algebras and group algebras of finite groups. For this particular class of algebras we present a construction of an upper bound for the finitistic dimension which is due to Lueck.