Related papers: A generalization of the brauer algebra
We study the Leibniz $n$-algebra $\textbf{U}_n(\mathfrak{L})$, whose multiplication is defined via the bracket of a Leibniz algebra $\mathfrak{L}$ as $[x_1,\dots,x_n]=[x_1,[\dots, [x_{n-2},[x_{n-1},x_n]]\dots]]$. We show that…
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 prove a semisimplicity criterion for a large class of algebras by a new method. This can be applied to Brauer, BMW, and $q$-Brauer algebras.
The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An…
In this paper, we give a necessary and sufficient condition for a cyclotomic Brauer algebra being semisimple. This generalizes previous result for a Brauer algebra.
We show that an arbitrary algebra ${ A}$, (of arbitrary dimension, over an arbitrary base field and any identity is not suppose for the product), is semisimple if and only if it has zero annihilator and admits a semi-division linear basis.…
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…
The radical of the Brauer algebra B_f^x is known to be non-trivial when the parameter x is an integer subject to certain conditions (with respect to f). In these cases, we display a wide family of elements in the radical, which are…
We introduce the marked Brauer algebra and the marked Brauer category. These generalize the analogous constructions for the ordinary Brauer algebra to the setting of a homogeneous bilinear form on a $\mathbb{Z}_2$-graded vector space. We…
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 construct a naturally $\mathbb Z$-graded algebra $\mathscr G_n(\delta)$ over $R$ with KLR-like relations and give an explicit isomorphism between $\mathscr G_n(\delta)$ and $\mathscr B_n(\delta)$, the Brauer algebras over $R$, when $R$…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie n-algebras. We also consider the…
We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra of simply-laced…
A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. A subalgebra is narrow if the restrictions of all non-trivial simple modules to…
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…
From the Levi's Theorem it is known that every finite dimensional Lie algebra over a field of characteristic zero is decomposed into semidirect sum of solvable radical and semisimple subalgebra. Moreover, semisimple part is the direct sum…
The goal of this paper is to describe the structure of finite-dimensional semi-simple Leibniz algebras in characteristic zero. Our main tool in this endeavor are hemi-semidirect products. One of the major results of this paper is a…
We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show…
We introduce a Brauer type algebra $B_G (\Upsilon) $ associated with every pseudo reflection group and every Coxeter group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized…