On selfinjective algebras without short cycles in the component quiver

Abstract

We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.

Selfinjective algebras having a generalized standard family of quasi-tubes maximally saturated by simple and projective modules

“…Namely, every algebra Λ is a quotient algebra of a selfinjective algebra A with Γ A having a generalized standard stable tube (see [28], [29]). We refer to [6], [13], [14], [16] for some work on the structure of selfinjective algebras having generalized standard families of quasi-tubes.…”