More Examples of Algebraic Quantum Hypergroups

Abstract

We present in this paper a family of algebraic quantum hypergroups. Fix a natural number n ∈ ℕ. Let Hn be an infinite-dimensional vector space with a basis {Xp,i, Yq,j | p, q ∈ ℤ, i, j ∈ {0, 1, 2, ⋯ n}}. Then we consider the new multiplication on Hn with structure constants \(\{c^k_{pij}\mid p\in \mathbb{Z}, i, j, k\in \{0, 1, 2, \dots n\}\}\) and present a new method of constructing algebraic quantum hypergroups which is very different from the one in Van Daele and Wang (Math Scand 108(2):198–222, 2011). Finally, we give an explicit example to explain our procedure.