Erdmann, Karin Holm, Thorsten Iyama, Osamu Schröer, Jan
Published in
Advances in Mathematics

Given a representation-finite algebra B and a subalgebra A of B such that the Jacobson radicals of A and B coincide, we prove that the representation dimension of A is at most three. By a result of Igusa and Todorov, this implies that the finitistic dimension of A is finite.

Jue, Brian
Published in
Open Mathematics

Let $$\mathbb{K}$$ be an algebraically closed field. Consider a finite dimensional monomial relations algebra $$\Lambda = {{\mathbb{K}\Gamma } \mathord{\left/ {\vphantom {{\mathbb{K}\Gamma } I}} \right. \kern-\nulldelimiterspace} I}$$ of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path...

Herzog, Ivo
Published in
Advances in Mathematics

A morphism f : M → N of left R-modules is a phantom morphism if for any morphism g : A → M , with A finitely presented, the composition fg factors through a projective module. Equivalently, Tor 1 ( X , f ) = 0 for every right R-module X. It is proved that every R-module possesses a phantom cover, whose kernel is pure injective. If mod ̲ - R is the ...

Wei, Jiaqun
Published in
Advances in Mathematics

The notion of Igusa–Todorov algebras is introduced in connection with the (little) finitistic dimension conjecture, and the conjecture is proved for those algebras. Such algebras contain many known classes of algebras over which the finitistic dimension conjecture holds, e.g., algebras with the representation dimension at most 3, algebras with radi...

Bahri, A. Bendersky, M. Cohen, F.R. Gitler, S.
Published in
Advances in Mathematics

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of Goresky–MacPherson...

Craw, Alastair Velez, Alexander Quintero

This paper constructs cellular resolutions for classes of noncommutative algebras, analogous to those introduced by Bayer-Sturmfels in the commutative case. To achieve this we generalise the dimer model construction of noncommutative crepant resolutions of toric algebras in dimension three by associating a superpotential and a notion of consistency...

Dugas, A. Huisgen-Zimmermann, B.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{

Dugas, A. Huisgen-Zimmermann, B.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{

Dugas, A. Huisgen-Zimmermann, B.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{

Dugas, A. Huisgen-Zimmermann, B.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{