Allegretti, Dylan G. L.
Published in
Selecta Mathematica

We consider a cluster variety associated to a triangulated surface without punctures. The algebra of regular functions on this cluster variety possesses a canonical vector space basis parametrized by certain measured laminations on the surface. To each lamination, we associate a graded vector space, and we prove that the graded dimension of this ve...

Ramos, Eric White, Graham
Published in
Selecta Mathematica

For fixed positive integers n and k, the Kneser graph KGn,k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$KG_{n,k}$$\end{document} has vertices labeled by k-element su...

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...

Bissinger, Daniel
Published in
Forum Mathematicum

Inspired by recent work of Carlson, Friedlander and Pevtsova concerning modules for p-elementary abelian groups E r {E_{r}} of rank r over a field of characteristic p > 0 {p>0} , we introduce the notions of modules with constant d-radical rank and modules with constant d-socle rank for the generalized Kronecker algebra 𝒦 r = k Γ r {\mathcal{K}_{r...

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
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 ...

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
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...

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

Chindris, Calin Kinser, Ryan
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...