相关论文: Discriminants of Brauer algebras
In this paper, we compute Gram determinants associated to all cell modules of quantized walled Brauer algebras $\mathscr B_{r, t}(\rho, q)$ over an arbitrary field $\kappa$. Suppose $e$ is the quantum characteristic of $q^2$. We classify…
For each natural number n greater than 1, we define an algebra satisfying many properties that one might expect to hold for a Brauer algebra of type Cn. The monomials of this algebra correspond to scalar multiples of symmetric Brauer…
We analyze cyclic cell modules over walled Brauer algebra in terms of a certain normal form. The latter allows us to decompose the algebra into the generating set and annihilator ideal of a certain cyclic vector. In addition, we show that…
In this paper, we compute the Gram determinants associated to each cell module of the Birman-Wenzl algebras. As a by-product, we give the necessary and sufficient condition for semisimple Birman-Wenzl algebras over an arbitrary field.
We consider central simple $K$-algebras which happen to bedifferential graded $K$-algebras. Two such algebras $A$ and $B$are considered equivalent if there are bounded complexes of finite dimensional$K$-vector spaces $C_A$ and $C_B$ such…
Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to an arbitrary (not necessarily commutative) ring of finite rank over the integers using techniques from linear algebra. Our…
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…
For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the…
In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This also allows us to calculate the structure constants of multiplication over the Grothendieck ring…
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…
In this paper, we go on Rui-Xu's work on cyclotomic Birman-Wenzl algebras $\W_{r, n}$ in \cite{RX}. In particular, we use the representation theory of cellular algebras in \cite{GL} to classify the irreducible $\W_{r, n}$-modules for all…
We determine the decomposition matrices of the Brauer algebra over the complex field.
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…
The differential Brauer monoid of a differential commutative ring R s defined. Its elements are the isomorphism classes of differential Azumaya R algebras with operation from tensor product subject to the relation that two such algebras are…
In this paper, we construct the permutation modules and Young modules for Brauer algebras of type $C$ by extending the representation theory of the group algebra of hyperoctahedral groups. Additionally, we develop a stratifying system for…
In a recent paper Cohen, Liu and Yu introduce the Type $C$ Brauer algebra. We show that this algebra is an iterated inflation of hyperoctahedral groups, and that it is cellularly stratified. This gives an indexing set of the standard…
In this paper we study the partial Brauer $\mathbb{C}$-algebras $\mathfrak{R}_n(\delta,\delta')$, where $n \in \mathbb{N}$ and $\delta,\delta'\in\mathbb{C}$. We show that these algebras are generically semisimple, construct the Specht…
Brauer algebras form a tower of cellular algebras. There is a well-defined notion of limiting blocks for these algebras. In this paper we give a complete description of these limiting blocks over any field of positive characteristic. We…
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.
The centralizer algebra of the action of the unitary group on the real tensor powers of its natural module, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with…