2D Toda Chain and Associated Commutator Identity

摘要

Developing the observation made in [1], we show that a simple identity of the commutator type on an associative algebra is in one-to-one correspondence to the 2D (infinite) Toda chain. We introduce a representation of the elements of an associative algebra that, under some generic conditions,enables the derivation of the Toda chain equation and its Lax pair from the given commutator identity.