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.

Stating a two-parameter class of examples, a — positive — answer is given to the question “Are there any nontrivial hypergroups on Z?” . 1. Background and Introduction In 1989 Zeuner [14] proved that no nontrivial hypergroups (i. e. not the group) exist on the set of real numbers R. Five years later Rösler [5] showed that by weakening the axioms by considering signed hypergroups some of these s...

An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is char...

This paper aims to show that the amenability of K1 ×K2 is equivalent to the following condition: “If φ is a continuous positive definite function defined on K1 ×K2 and φ ≥ 0 then the constant function 1K1×K2 belongs to the spectrum of φ”, which K1 and K2 are locally compact hypergroups as defined by R. Jewett [1], with convolutions ∗1, ∗2 respectively.Our study deals with the cases of exponenti...

Fortified Transposition Hypergroups appeared during the study of the theory of Formal Languages and Automata from the point of view of the hypercompositional structures theory. This paper studies the subhypergroups of these hypergroups and presents properties of their closed, symmetric, normal and reflexive subhypergroups.

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25