Zobrazeno 1 - 10
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pro vyhledávání: '"SCHIFFLER, RALF"'
Let $A$ be the path algebra of a quiver of Dynkin type $\mathbb{A}_n$. The module category $\text{mod}\,A$ has a combinatorial model as the category of diagonals in a polygon $S$ with $n+1$ vertices. The recently introduced notion of almost rigid mod
Externí odkaz:
http://arxiv.org/abs/2410.04627
In previous work, we associated a module $T(i)$ to every segment $i$ of a link diagram $K$ and showed that there is a poset isomorphism between the submodules of $T(i)$ and the Kauffman states of $K$ relative to $i$. In this paper, we show that the p
Externí odkaz:
http://arxiv.org/abs/2409.11287
We study maximal almost rigid modules over a gentle algebra $A$. We prove that the number of indecomposable direct summands of every maximal almost rigid $A$-module is equal to the sum of the number of vertices and the number of arrows of the Gabriel
Externí odkaz:
http://arxiv.org/abs/2408.16904
We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and Ovsienko. Th
Externí odkaz:
http://arxiv.org/abs/2408.06902
To every knot (or link) diagram K, we associate a cluster algebra A that contains a cluster x with the property that every cluster variable in x specializes to the Alexander polynomial of K. We call x the knot cluster of A. Furthermore, there exists
Externí odkaz:
http://arxiv.org/abs/2405.16592
Snake graphs are a class of planar graphs that are important in the theory of cluster algebras. Indeed, the Laurent expansions of the cluster variables in cluster algebras from surfaces are given as weight generating functions for 1-dimer covers (or
Externí odkaz:
http://arxiv.org/abs/2306.14389
Autor:
Duan, Bing, Schiffler, Ralf
Let $\mathscr{C}$ be the category of finite-dimensional modules over a simply-laced quantum affine algebra $U_q(\widehat{\mathfrak{g}})$. For any height function $\xi$ and $\ell\in \mathbb{Z}_{\geq 1}$, we introduce certain subcategories $\mathscr{C}
Externí odkaz:
http://arxiv.org/abs/2305.08715
Autor:
Schiffler, Ralf
This paper is a slightly extended version of the talk I gave at the Open Problems in Algebraic Combinatorics conference at the University of Minnesota in May 2022. We introduce two strict order relations on lattice paths and formulate several open pr
Externí odkaz:
http://arxiv.org/abs/2302.02185
Autor:
Schiffler, Ralf, Serhiyenko, Khrystyna
Dimer tree algebras are a class of non-commutative Gorenstein algebras of Gorenstein dimension 1. In previous work we showed that the stable category of Cohen-Macaulay modules of a dimer tree algebra $A$ is a 2-cluster category of Dynkin type $\mathb
Externí odkaz:
http://arxiv.org/abs/2211.14580
Autor:
Schiffler, Ralf, Serhiyenko, Khrystyna
Publikováno v:
In Journal of Algebra 15 December 2024 660:91-133