Quantisations of the Volterra hierarchy

Abstract In this paper, we explore a recently emerged approach to the problem of quantisation based on notion ideals. We explicitly prove that nonabelian Volterra together with whole hierarchy its symmetries admits deformation quantisation. show all odd-degree admit also non-deformation discuss for periodic including their quantum Hamiltonians, central elements quantised algebras, and demonstrate super-integrability systems obtained. system period 3 bi-quantum structure, which can be regarded as classical bi-Hamiltonian structure.