Jiao, Pengjie
Published in
Forum Mathematicum

For an interval finite quiver Q, we introduce a class of flat representations. We classify the indecomposable projective objects in the category rep ( Q ) {\mathrm{rep}(Q)} of pointwise finite dimensional representations. We show that an object in rep ( Q ) {\mathrm{rep}(Q)} is projective if and only if it is a direct sum of countably generated...

Liu, Yu Zhe Zhang, Chao
Published in
Acta Mathematica Sinica, English Series

An algebra A is called derived-unique provided that any algebra which is derived equivalent to A is necessarily Morita equivalent to A. We classify derived-unique gentle algebras with at most one cycle using the combinatorial invariant introduced by Avella-Alaminos and Geiss.

Guo, Jin Yun Luo, Deren

In this paper we study a class of algebras having $n$-dimensional pyramid shaped quiver with $n$-cubic cells, which we called $n$-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic $n$-Auslander absolutely $n$-complete algebras introduced by Iyama. We show that the projective resolution of the simples of $n$-cub...

Zhang, Chao
Published in
Science China Mathematics

Bongartz (2013) and Ringel (2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly studies this "no gaps" theorem as to cohomological length for the bounded derived category Db(A) of a gentle algebra A: if there is an inde...

Ovsienko, Valentin Tabachnikov, Serge

International audience

Asashiba, Hideto Escolar, Emerson G. Hiraoka, Yasuaki Takeuchi, Hiroshi

The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persistence module $M$ on $CL_n(\tau)$ as a morphism between zigzag modules, which can be expressed in a blo...

Chindris, Calin Kinser, Ryan

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ to a product of simpler moduli spaces via a finite and birational map. Furthermore, this morphism i...

Maslovarić, Marcel Seppänen, Henrik
Published in
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We generalize the notion of multi-Gieseker semistability for coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves using a functorial method that realizes these as subschemes of moduli spaces of representations of a twisted quiver, depending on Q, with...

Hochenegger, Andreas Kalck, Martin Ploog, David

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.

Zito, Stephen
Published in
Archiv der Mathematik

Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E. We provide a short proof to a conjecture by Assem and Zacharia concerning properties of modB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage...