A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in He...

Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite q×q-matrices over R,C,H were introduced recently by Rösler. These convolutions depend on some continuous parameter, generate commutative hypergroup structures and have Bessel functions of matrix argument as characters. Here, we first study the rich algebraic structure of these hypergroups. In...

measure always exists on a commutative hypergroup K, and there always exists a 'Plancherel measure' on the dual space K of equivalence classes of irreducible representations of K, with respect to which Plancherel's formula holds for Fourier transforms. In contrast with the case of a locally compact abelian group, however, the Plancherel measure is not necessarily a Haar measure on K, and K need...

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...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

This paper presents the study of algebraic structures equipped with inverted associativity axiom. Initially, definition left and right almost-groups is introduced afterwards, focused on more general structures, which are almost-hypergroups their enumeration in cases order 2 3. The outcomes these enumerations compared corresponding hypergroups reveal interesting results. Next, fundamental proper...

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...

i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]longrightarrow[a+x=x].$i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved thatif the order is less than 9, they are strongly canonical (see [13]). in this paperwe obtain the sequences of fuzzy sets and of join spaces determined (see [8])by all i.p.s. hypergroups of order seven. for the meaning ...

We explain how one can construct a class of discrete hypergroups which are non-unimodular. They arise as double coset hypergroups induced by the transitive action of a non-unimodular group of permutations on an innnite set. A concrete example is given in terms of the aane group of a homogeneous tree.

We explicitly construct the convolution hypergroups of spheres in the vertex graphs of the classical Platonic solids, their character tables, and the structure of their dual signed hypergroups. This allows us to easily determine certain aspects of the random walks on these graphs. The character tables share many of the pleasant properties of character tables of finite groups.