Related papers: Brauer-Thrall theory for maximal Cohen-Macaulay mo…
Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will…
A few years ago, Huneke and Leuschke proved a theorem which solved a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at…
In this paper, we determine the structure and representation theory of the Brauer algebra associated to a complex reflection group (here called the Brauer-Chen algebra), defined by Chen in 2011. We prove that it is semisimple and provide a…
Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of this category and thereby extend a result of Leuschke to the…
We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules over a complete Cohen-Macaulay local ring. We define a topology on the space of isomorphism classes of indecomposable maximal Cohen-Macaulay modules and…
Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal $\tau$-tilting infinite algebras. In particular, we treat minimal $\tau$-tilting infinite algebras as a modern counterpart of minimal…
The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
The Brauer-Chen algebra is a generalization of the algebra of Brauer diagrams to arbitrary complex reflection groups, that admits a natural monodromic deformation. We determine the generic representation theory of the first non trivial…
Turner's Conjecture describes all blocks of symmetric groups and Hecke algebras up to derived equivalence in terms of certain double algebras. With a view towards a proof of this conjecture, we develop a general theory of Turner doubles. In…
In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext modules. One of the applications shows that the…
In this short note, we state a stable and a $\tau$-reduced version of the second Brauer-Thrall Conjecture. The former is a slight strengthening of a brick version of the second Brauer-Thrall Conjecture raised by Mousavand and…
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…
In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…
In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the set of isomorphism classes of maximal Cohen--Macaulay modules…
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,…
For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the…
Let $A$ be an abelian variety over a field finitely generated over $\mathbb{Q}$. We show that the finiteness of the $\ell$-primary torsion subgroup of the higher Brauer group is a sufficient criterion for the Tate conjecture to hold.…
We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands…
We show that Colliot-Th\'el\`ene's conjecture on 0-cycles of degree 1 implies finiteness for the u-invariant of the function field of a curve over a totally imaginary number field and period-index bounds for the Brauer groups of arbitrary…