Quantum Lie algebra of currents - the universal algebraic structure of symmetries of completely integrable dynamical systems (Q1824774)

It is shown that the Lie algebra given by the following commutator relations \[ [\rho_ j,\rho_ k]=0,\quad [\rho_ j,J_ k]=j\rho_{j+k},\quad [J_ j,J_ k]=(j-k)J_{j+k} \] gives a universal description for algebras generated by symmetries of completely integrable systems. A similar result was also obtained by the reviewer [J. Phys. 21, No.9, 1951-1957 (1988)].