Conformal inclusions of chiral conformal field theories, or more generally quantum are described in the von Neumann algebraic setting by nets subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation mind, we study a purely subfactor theoretical context certain class braided discrete subfactors an additional commutativity constraint, tha...

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups...

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly p...

Different partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations and on H we investigate when the hypergroups associated with the relations ∩ , ∪ and are reduced. We also determine when the cartesian product of two hypergroupo...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...