Related papers: Normal form for the walled Brauer algebra: constru…
It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…
In previous two papers, we defined fractional Brauer configuration algebras and developed their covering theory. In this paper, we study the representation theory of fractional Brauer graph algebras of type MS, a special class of fractional…
We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non…
Following Nazarov's suggestion~\cite{Naz1}, we refer to the cyclotomic Nazarov-Wenzl algebra as the cyclotomic Brauer algebra. When the cyclotomic Brauer algebra is isomorphic to the endomorphism algebra of $M_{I_i, r}$-- the tensor product…
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…
In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…
We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables…
This paper surveys and illustrates geometric methods for constructing normal bases allowing efficient finite field arithmetic. These bases are constructed using the additive group, the multiplicative group and the Lucas torus. We describe…
We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner…
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…
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…
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem.…
This paper investigates the representation theory of the algebra of partially transposed permutation operators, $\mathcal{A}^d_{p,p}$, which provides a matrix representation for the abstract walled Brauer algebra. This algebra has recently…
We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley's structure theorem for algebraic groups.
For each square complex matrix, V. I. Arnold constructed a normal form with the minimal number of parameters to which a family of all matrices B that are close enough to this matrix can be reduced by similarity transformations that smoothly…
We construct the algebra of fractions of a Weak Bialgebra relative to a suitable denominator set of group-like elements that is `almost central', a condition we introduce in the present article which is sufficient in order to guarantee…
We define a degenerate affine version of the walled Brauer algebra, that has the same role plaid by the degenerate affine Hecke algebra for the symmetric group algebra. We use it to prove a higher level mixed Schur-Weyl duality for gl_N. We…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
We establish a framework for cellularity of algebras related to the Jones basic construction. Our framework allows a uniform proof of cellularity of Brauer algebras, ordinary and cyclotomic BMW algebras, walled Brauer algebras, partition…
The Poincare'-Dulac normal form of a given resonant system is in general non unique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this note we give an algorithm, based on the Lie algebraic…