since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

In this note we revisit the notion of amenable representation type introduced by Gábor Elek. We show that tame hereditary path algebras quivers extended Dynkin over any field k $k$ are type. This verifies a conjecture Elek, which draws similarities to tame-wild dichotomy, for another class algebras. also wild acyclic finite fields not amenable.

Abstract Birge Huisgen-Zimmermann calls a finite dimensional algebra homologically tame provided the little and big finitistic dimension are equal finite. The question formulated in title has been discussed by her paper “Representation-tame algebras need not be tame”, looking for any r ≥ 1 at sequence of Λ m with + . As we will show, also is It follows that contrary to assertion, all tame.

We determine the derived representation type of Nakayama algebras and prove that a tame algebra without simple projective module is gentle or equivalent to some skewed-gentle algebra, as consequence, we its singularity category.