An extended trace identity and applications. (English) Zbl 1172.70009

From the abstract: For the loop algebras in the form of non-square matrices, their commuting operations can be used to set up linear isospectral problems. In order to look for Hamiltonian structures of the corresponding integrable evolution hierarchies of equations, an extended trace identity is obtained by means of commutators, which undoes the constraint on the known trace identity proposed by G. Tu [J. Math. Phys. 30, No. 2, 330–338 (1989; Zbl 0678.70015)], and has an obvious simplicity in applications compared with the quadratic-form identity given by F. Guo and Y. Zhang [J. Phys. A, Math. Gen. 38, No. 40, 8537–8548 (2005; Zbl 1077.37045)].


70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
37N05 Dynamical systems in classical and celestial mechanics
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