The finitistic dimension of an Artin algebra with radical square zero

Abstract

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