It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated...

Hypergroups are generalizations of groups. If this binary operation is taken to be multivalued, then we arrive at a hypergroup. The motivation for generalization of the notion of group resulted naturally from various problems in non-commutative algebra, another motivation for such an investigation came from geometry. In various branches of mathematics we encounter important examples of topologi...

In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.

In this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.We also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

Abstract The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of normal First we define concept zero-divisors over hypermodule based it introduce class hypermodules, one divisible After presenting some their fundamental properties, will show that R -hypermodules M coincide whenever hyperring with no . Finally...

We show that the sum of two adjoint orbits in the Lie algebra of an exponential Lie group coincides with the Campbell-Baker-Hausdorff product of these two orbits. Introduction N. Wildberger and others have recently investigated the structure of the hypergroup of the adjoint orbits in relation with the class hypergroup of compact Lie groups. A generalization of the notion of this type of hypergr...

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are rev...

Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using abelian hypergroups and an associated classical simulation theorem (a la Gottesman-Knill). Using these tools, we develop the first provably efficient quantu...

A discrete DJS-hypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a generalized quantum Gelfand pair, where the role of the quantum subgroup is taken over by a two-sided coideal in the dual Hopf algebra. The paper starts with...