In this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke $*$-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative $*$-algebra if and only if K is a locally compact group.

中文翻译：

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局部紧致超群上的Hecke **代数

在本文中，对于离散超群K及其子超群H，我们发起相关的Hecke$*$-代数，它是经典之一的扩展，并研究其基本性质。尤其是，我们给出了使该代数具有关联性的充要条件（称为（β））。此外，我们证明了这种新结构是一种联想$*$-代数，当且仅当K是局部紧凑群时。