Publication: Hyperdeterminants as integrable discrete systems

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Title Hyperdeterminants as integrable discrete systems
Authors/Editors* SP Tsarev, T Wolf
Where published* J. Phys. A: Math. Theor., arXiv:0903.3864 (nlin.SI)
How published* Other
Year* 2009
Volume 42
Number doi: 10.1088/1751-8113/42/45/454023
Pages 9
Publisher IOP
Keywords hyperdeterminants, discrete differential geometry, computer algebra
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 implies 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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