Related papers: Generalized Auslander-Reiten conjecture and derive…

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of…

We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.

We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a…

A main purpose of this paper is to prove that the class of finite dimensional algebras which verify Han's conjecture is closed under split bounded extensions.

Let $\mathscr{C}$ be an $n$-exangulated category. In this note, we show that if $\mathscr{C}$ is locally finite, then $\mathscr{C}$ has Auslander-Reiten $n$-exangles. This unifies and extends results of Xiao-Zhu, Zhu-Zhuang, Zhou and…

We prove that the Center Conjecture passes to the Artin groups whose defining graphs are cones, if the conjecture holds for the Artin group defined on the set of the cone points. In particular, it holds for every Artin group whose defining…

Let $\cal C$ be a $(d+2)$-angulated category. In this note, we show that if $\cal C$ is a locally finite, then $\cal C$ has Auslander-Reiten $(d+2)$-angles. This extends a result of Xiao-Zhu for triangulated categories.

We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the…

We prove some new formulae for the derivatives of the generalized Gegenbauer polynomials associated to the Lie algebra $A_2$.

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.

In this article, we introduce congruential Euler numbers, which are a further generalization of generalized Euler numbers. We prove the $p$-adic congruences of congruential Euler numbers, which include answers to a conjecture related to…

In this paper, we prove a conjecture of Schnell in the surface case.

We provide a framework for part of the homological theory of Z-algebras and their generalizations, directed towards analogues of the Auslander-Gorenstein condition and the associated double Ext spectral sequence that are useful for…

We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a…

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

In this article we study derived (auto)equivalences of generalized Kummer varieties $\mathrm{Kum}^n(A)$. We provide an answer to a question raised by Namikawa by showing that the generalized Kummer varieties $\mathrm{Kum}^n(A)$ and…

We resolve Manin's conjecture for all Ch\^atelet surfaces over $\mathbb{Q}$.

We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.

We use $t$-structures on the homotopy category $K^b(R-mod)$ for an artin algebra $R$ and Watts' representability theorem to give an existence proof for Auslander-Reiten sequences of $R$-modules.

Inspired by the work of Rostam, we establish an explicit categorical equivalence between affine Yokonuma-Hecke algebras and quiver Hecke algebras associated to disjoint copies of quivers of (affine) type $A,$ generalizing Rouquier's…