Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra

The higher rank Askey-Wilson algebra was recently constructed in the n-fold tensor product of U-q (sl(2)). In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow to simplify calculations significantly. At the same time, this provides a proof of the corresponding relations for the higher rank q-Bannai-Ito algebra.