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.
Published in Algebras and Representation Theory
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 resolutions of the simples of n-cubic pyramid ...
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...
Published in Algebras and Representation Theory
We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the not...
Published in Japan Journal of Industrial and Applied Mathematics
The theory of persistence modules on the commutative ladders CLn(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CL_n(\tau )$$\end{document} provides an extension of ...
Published in Mathematische Annalen
Consider a finite-dimensional algebra A and any of its moduli spaces M(A,d)θss\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {M}}}(A,\mathbf {d})^{ss}_{\the...
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...
Published in Mathematische Zeitschrift
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.
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...
Published in Algebras and Representation Theory
Let J(C) be the poset of order ideals of a cominuscule poset C where C comes from two of the three infinite families of cominuscule posets or the exceptional cases. We show that the Auslander-Reiten translation τ on the Grothendieck group of the bounded derived category for the incidence algebra of the poset J(C), which is called the Coxeter transf...
