A skew group ring of Z/2Z over U(sl_2), Leonard triples and odd graphs

We employ a skew group ring of Z/2Z over U(sl₂) to construct modules over the universal Bannai–Ito algebra. Furthermore, we characterize the conditions under which the defining generators act as Leonard triples on these modules. As a combinatorial realization, we establish a surjective algebra homomorphism from the universal Bannai–Ito algebra to the Terwilliger algebra of an odd graph. This homomorphism provides a unified description of Leonard triples on all irreducible modules over the Terwilliger algebra.