# Questions tagged [hypergroups]

The hypergroups tag has no usage guidance.

**16**

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**5**answers

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### What are hypergroups and hyperrings good for?

I came across the concept of a hyperring in two recent papers by Connes and Consani (From monoids to hyperstructures: in search of an absolute arithmetic and The hyperring of adèle classes). It's a ...

**11**

votes

**3**answers

815 views

### To what extent has the Haar measure been generalized?

It is known that all locally compact groups, and therefore compact groups, have a left-invariant Haar measure which is unique up to scalar constant, also a right-invariant one. Is there a strictly ...

**7**

votes

**2**answers

524 views

### Groupoids and hypergroups

There are two generalizations of usual groups: groupoids, where the multiplication operation becomes "partial", and hypergroups, for which the result of multiplying two elements is a probability ...

**6**

votes

**1**answer

425 views

### When does a matrix define a convolution operator on a hypergroup?

Let $H$ be a discrete hypergroup. Suppose I have a matrix $A=(A_{x,y})$ indexed over $H$ with nonnegative entries which defines a bounded operator on $\ell^2(H)$. When does there exist $f\in\ell^1(H)$ ...

**5**

votes

**1**answer

170 views

### The (Hecke) double coset von Neumann algebra

It it well-known in the von Neumann algebra theory that for $\Gamma$ a non-trivial countable group, the von Neumann algebra $L(\Gamma)$ generating by $\Gamma$ acting by left multiplication on $l^2(\...

**4**

votes

**1**answer

242 views

### Classification of finite abelian hypergroups and table algebras

Update: Originally, I formulated this question for finite abelian hypergroups, but in a discussion with Geoff Robinson below I realized that the abelian hypergroups defined below are equivalent to ...

**3**

votes

**0**answers

173 views

### Groups with probability measures

Are there algebraic structures that integrate groups with probability measures? For instance, can the closure operation on a group be assigned a probability that says "how much" a member belongs to ...

**1**

vote

**1**answer

205 views

### Is a prime index inclusion of finite groups, separating?

Let $(H \subset G)$ be an inclusion of finite groups.
Let $\{ g_i \ \vert \ i \in I=[1, \dots ,n] \}$ a subset of $G$ of double coset representatives, i.e. $$G = \coprod_{i \in I} Hg_iH$$
On the ...

**1**

vote

**0**answers

149 views

### Amenable hypergroups

I needed some information about the intersection of the kernels of invariant means on hypergroups. So I read the discussion made for the question " The kernel of all invariant means " which answer my ...