Related papers: The decomposition matrices of the Brauer algebra o…
In this paper, we calculate decomposition matrices of the Birman-Murakami-Wenzl algebras over $\mathbb C$.
We determine the blocks of the periplectic Brauer algebra over any field of odd characteristic.
We define a Brauer group for differential graded algebras over differential graded graded-commutative or commutative base rings. Based on previous work we give an explicit classification of dg-fields, and compute the so-defined Brauer group…
This paper gives two results on the simple modules for the Brauer algebra over the complex field. First we describe the module structure of the restriction of all simple modules. Second we give a new geometrical interpretation of Ram and…
Using the combinatorial information of a Brauer configuration is possible to compute each entry of the Cartan matrix of the algebra associated to the Brauer configuration.
In this paper all two-term tilting complexes over a Brauer tree algebra with multiplicity one are described using a classification of indecomposable two-term partial tilting complexes obtained earlier in a joint paper with M. Antipov. The…
We give a closed formula for the graded decomposition numbers of the blob algebra over a field of characteristic zero at a root of unity.
Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph…
We determine the Jordan-Holder decomposition multiplicities of projective and cell modules over periplectic Brauer algebras in characteristic zero. These are obtained by developing the combinatorics of certain skew Young diagrams. We also…
Following Nazarov's suggestion, the cyclotomic Nazarov-Wenzl algebra is referred to as the cyclotomic Brauer algebra. This paper focuses on computing the decomposition numbers of the cyclotomic Brauer algebra over $\mathbb{C}$ with…
In this article we calculate two aspects of the representation theory of a Brauer configuration algebra: its Cartan matrix, and the module length of its associated indecomposable projective modules. Then we introduce the concept of…
The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…
In this paper we describe all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an…
We study the evaluation maps given by elements of the Brauer group of varieties over local fields. We show constancy of the aforementioned maps in several interesting cases.
The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…
We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and…
We study K3 surfaces with complex multiplication following the classical work of Shimura on CM abelian varieties. After we translate the problem in terms of the arithmetic of the CM field and its id\`{e}les, we proceed to study some abelian…
A complete classification of two-dimensional algebras over algebraically closed fields is provided
We compute the Brauer group of the moduli stack of elliptic curves over the integers, localizations of the integers, finite fields of odd characteristic, and algebraically closed fields of characteristic not $2$. The methods involved…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.