Related papers: Projective indecomposable modules and quivers for …
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
Persistence modules serve as the algebraic foundation for topological data analysis, typically studied as representations of posets over a field. This article extends the structural and decomposition theory of persistence modules to the…
We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra,…
Using diagrammatic methods, we define a quiver algebra depending on a prime p and show that it is the algebra underlying the category of tilting modules for SL(2) in characteristic p. Along the way we obtain a presentation for morphisms…
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
For a quiver with potential $(Q,W)$ with an action of a finite cyclic group $G$, we study the skew group algebra $\Lambda G$ of the Jacobian algebra $\Lambda = \mathcal P(Q, W)$. By a result of Reiten and Riedtmann, the quiver $Q_G$ of a…
We construct all finite irreducible modules over Lie conformal superalgebras of type K
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…
We study the partial Brauer monoid and its planar submonoid, the Motzkin monoid. We conduct a thorough investigation of the structure of both monoids, providing information on normal forms, Green's relations, regularity, ideals, idempotent…
Let $g$ be a finite dimensional simple Lie algebra. Denote by $\mathcal B$ the category of all bounded weight $g$-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of…
In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the…
We study the bialgebra structures on quiver coalgebras and the monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural…
We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the…
We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of $r$-invertible $r$-ideals for certain ideal systems $r$) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero…
A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first order differential calculus on such a…
Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a…
In this paper, we shall use a method based on the theory of extensions of left-symmetric algebras to classify complete left-invariant affine real structures on solvable non-unimodular three-dimensional Lie groups.
In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…