The finitistic dimension of an Artin algebra with radical square zero

Abstract

We investigate the inequality Findim ⁡ Λ o p ≤ dell ⁡ Λ \operatorname {Findim} \Lambda ^{op} \leq \operatorname {dell} \Lambda between the finitistic dimension and the delooping level of an Artin algebra Λ \Lambda , and whether equality holds in general. We prove that equality Findim ⁡ Λ o p = dell ⁡ Λ \operatorname {Findim} \Lambda ^{op} = \operatorname {dell} \Lambda always holds for Artin algebras with radical square zero.