Related papers: On pseudofrobenius imprimitive association schemes
In "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, we introduce the Frobenius P-categories giving two quite different definitions of them. In this paper, we exhibit a third equivalent definition based on the form of the…
A Frobenius difference field is an algebraically closed field of characteristic $p>0$, enriched with a symbol for $x \mapsto x^{p^m}$. We study a sentence or formula in the language of fields with a distinguished automorphism, interpreted…
In this article we continue with the study started in [1] of nearly Frobenius structures in some representative families of finite dimensional algebras, as the radical square zero algebras, string algebras and the toupie algebras. We prove…
An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if the thin residue of it forms a Klein group with respect to the relation product. It is proved that any…
We consider multicomponent local Poisson structures of the form $\mathcal P_3 + \mathcal P_1$, under the assumption that the third order term $\mathcal P_3$ is Darboux-Poisson and non-degenerate, and study the Poisson compatibility of two…
A finite group $P$ is said to be \emph{primary} if $|P|=p^{a}$ for some prime $p$. We say a primary subgroup $P$ of a finite group $G$ satisfies the \emph{Frobenius normalizer condition} in $G$ if $N_{G}(P)/C_{G}(P)$ is a $p$-group provided…
Minimal prime graphs are connected graphs on at least two vertices whose complements satisfy the following conditions: triangle-freeness, 3-colorability, and edge-maximality with respect to the latter two properties. These graphs are prime…
It is proved that with finitely many possible exceptions, each cyclotomic scheme over finite field is determined up to isomorphism by the tensor of 2-dimensional intersection numbers; for infinitely many schemes, this result cannot be…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…
If $\mathfrak{g}$ is a Frobenius Lie algebra, then for certain $F\in \mathfrak{g}^*$ the natural map $\mathfrak{g}\longrightarrow \mathfrak{g}^* $ given by $x \longmapsto F[x,-]$ is an isomorphism. The inverse image of $F$ under this…
An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\mathcal{K}$ if every its algebraic isomorphism to an $S$-ring over a group from $\mathcal{K}$ is induced by a combinatorial isomorphism. We prove that…
The aim of this paper is to apply character properties of Frobenius group to a local block form of an group algebra. We start by establishing a block form of Brauer permutation Lemma by using block participation of conjugate classes of a…
With a small suitable modification, dropping the projectivity condition, we extend the notion of a Frobenius algebra to grant that a Frobenius algebra over a Frobenius commutative ring is itself a Frobenius ring. The modification introduced…
Let C be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category C, that extend the corresponding graphs associated…
An imprimitive symmetric indecomposable association scheme of rank $5$ is said to be Higmanian. In the present paper, we prove a necessary and sufficient condition for a Higmanian association scheme with two nontrivial parabolics to be…
In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius…
Let $p$ be a prime number. We compute the trivial source character tables of finite Frobenius groups $G$ with an abelian Frobenius complement $H$ and an elementary abelian Frobenius kernel of order $p^2$. More precisely, we deal with all…
Classifying Frobenius algebras is a key question that has been addressed in various contexts. The structure of finite-dimensional Frobenius algebras depends on the base field and the dimension of the algebra, leading to different…
Let G be a group. The intersection graph G(G) of G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of G; and there is an edge between two distinct…
In this article, we classify all Buchsbaum simplicial affine semigroups whose complement in their (integer) rational polyhedral cone is finite. We show that such a semigroup is Buchsbaum if and only if its set of gaps is equal to its set of…