Related papers: Almost Commutative Terwilliger Algebras of Group A…

Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions. In this paper we…

Terwilliger algebras are a subalgebra of a matrix algebra that are constructed from association schemes over finite sets. In 2010, Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative. In that paper she gave…

Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. In 2010, Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions for a Terwilliger…

In [3], Hanaki defined the Terwilliger algebras of association schemes over a commutative unital ring. In this paper, we call the Terwilliger algebras of association schemes over a field $\mathbb{F}$ the Terwilliger $\mathbb{F}$-algebras of…

The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were briefly called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, the Terwilliger $\mathbb{F}$-algebras of direct…

A complete set of primitive orthogonal idempotents plays an important role in the representation theory of an associative algebra. In this paper, we construct a complete set of primitive orthogonal idempotents for any finite Brandt…

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that…

In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn decomposition. Particularly, we use this method to calculate…

The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, we study the Terwilliger $\mathbb{F}$-algebras of factorial…

The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [8]. In this paper, we study the Terwilliger $\mathbb{F}$-algebras of factorial…

Let $\mathbb{F}$ be an arbitrary field. In this paper, we continue studying the Terwilliger algebras of association schemes over $\mathbb{F}$ that were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [8]. We determine…

We give necessary and sufficient conditions for the Terwilliger algebra of a quasi-thin Schurian association scheme to coincide with: (a) the centralizer algebra of a point stabilizer of its automorphism group, and (b) its subspace $T^0$.…

An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents…

In this paper, we determine the dimension of the Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are triply transitive. Moreover, we give a complete characterization of the…

The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having…

Let $p$ denote a prime number. In this note, we focus on the modular Terwilliger algebras of association schemes defined in [3]. We define the primary module of a modular Terwilliger algebra of an association scheme and determine all its…

Let $J$ be an almost complex structure on a 4-dimensional and unimodular Lie algebra $\mathfrak{g}$. We show that there exists a symplectic form taming $J$ if and only if there is a symplectic form compatible with $J$. We also introduce…

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

Terwilliger algebras are finite-dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance-regular graphs. The Terwilliger algebras of the conjugacy class…

We give a description of the primitive central idempotents of the rational group algebra QG of a finite group G. Such a description is already investigated by Jespers, Olteanu and del R\'io, but some unknown scalars are involved. Our…