Invariance of selfinjective algebras of quasitilted type under stable equivalences

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.…”

Topological invariants of piecewise hereditary algebras

“…It is known that every self-injective algebra Λ is of polynomial growth if and only if Λ is a socle (geometric) deformation of an algebra of the formÂ/G where A is a tilted algebra of Dynkin type or Euclidean type or a tubular algebra, and G is an admissible infinite cyclic group of automorphisms of A ([46], [49]). Recently, the class of self-injective algebras of piecewise hereditary type has been the subject of many studies (see [15], [31], [37], [50], [51], [52]). …”