2D Toda chain and associated commutator identity
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Developing observation made in \cite{commut} we show that simple identity of the commutator type on an associative algebra is in one-to-one correspondence to 2D (infinite) Toda chain. We introduce representation of elements of associative algebra that, under some generic conditions, enables derivation of the Toda chain equation and its Lax pair from the given commutator identity.
💡 Research Summary
The paper establishes a precise one‑to‑one correspondence between a simple commutator identity in an associative algebra and the infinite‑dimensional two‑dimensional Toda chain. Starting from the elementary identity
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