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Hyperdeterminants as integrable discrete systems (2009)

Tsarev, Sergey ; Wolf, Thomas

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Publication Date: 2020-12-11

Description: 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 $2 \times 2 \times 2$ - 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 $2\times 2\times 2\times 2$ - hyperdeterminant.

Keywords: ddc:000

Language: English

Type: reportzib , doc-type:preprint

Format: application/pdf

Format: application/postscript

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