Related papers: Two-sided tilting complexes for generalized Brauer…

In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using a Brauer graph…

We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or…

Let $\Lambda$ be a hereditary algebra, $B_0=End_\Lambda(T_0)$ be a tilted algebra. We will construct tilting $B_0$-modules from tilting $\Lambda$-modules and use this result to show how tilting quivers of BB-tilted algebras can be obtained…

Let $A$ be an Auslander algebra of global dimension equal to 2. We provide a necessary and sufficient condition for $A$ to be a tilted algebra. In particular, $A$ is tilted if and only if pd$(\tau_{A}\Omega_{A}DA)\leq1$.

Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster…

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…

In this paper, we will define the Brauer algebras of Weyl types, and describe some propositions of these algebras. Especially, we prove the result of type $G_2$ to accomplish our project of Brauer algebras of non-simply laced types.

We prove the existence of tilting objects on generalized Brauer--Severi varieties, some relative flags and some twisted forms of relative flags. As an application we obtain tilting objects on certain homogeneous varieties of classical type…

We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebra, its partial analogue, walled Brauer algebra, its partial analogue, Temperley-Lieb algebra, its…

We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…

We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the…

A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined,…

In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for…

We use the maximal faces of the $m$-cluster complex of type A to describe the m-cluster tilted algebras of type A as quivers with relations. We then classify connected components of m-cluster tilted algebras of type A up to derived…

We introduce a plethora of skew algebroids on twistor spaces and describe the corresponding foliations. In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler…

Let $\mathbb{X}$ be a weighted projective line and $\operatorname{coh}\mathbb{X}$ the associated categoy of coherent sheaves. We classify the tilting complexes $T$ in $D^b(\operatorname{coh}\mathbb{X})$ such that $\tau^2 T\cong T$, where…

Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a…

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…

We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of…