Discrete subfactors include a particular class of infinite index and all finite ones. A discrete subfactor is called local when it braided fulfills commutativity condition motivated by the study inclusion Quantum Field Theories in algebraic Haag–Kastler setting. In Bischoff et al. (J Funct Anal 281(1):109004, 2021), we proved that every irreducible arises as fixed point under action canonical c...

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

in this paper, we de ne the concepts of general fuzzy recognizer, language recognized by a general fuzzy recognizer, the accessible and the coac- cessible parts of a general fuzzy recognizer and the reversal of a general fuzzy recognizer. then we obtain the relationships between them and construct a topology and some hypergroups on a general fuzzy recognizer.

In this paper, we present some connections between tree automaton theory and hyperstructure theory. In this regard, at first we construct some hyperoperations on the set of trees and, specially, prove that one of them creates a join space. Also, we define a hyperoperation on the states of a tree automaton and, based on the properties of the tree automaton, we show that the proposed hyperoperati...

We present an explicit product formula for the spherical functions of the compact Gelfand pairs (G,K1) = (SU(p+ q), SU(p)× SU(q)) with p ≥ 2q, which can be considered as the elementary spherical functions of one-dimensional K-type for the Hermitian symmetric spaces G/K with K = S(U(p)× U(q)). Due to results of Heckman, they can be expressed in terms of Heckman-Opdam Jacobi polynomials of type B...

Sunder and Wildberger (J. Algebr. Comb. 18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *action, then K arises from an association scheme. In this paper we will fi...

in this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...