Hyperdeterminants as integrable discrete systems

Details Hyperdeterminants as integrable discrete systems Hyperdeterminants as integrable discrete systems

2009-03-23

arxiv.org/abs/0903.3864v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstract

Scientific paper

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2x2x2x2-hyperdeterminant.

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