TY - GEN
A1 - Tsarev, Sergey
A1 - Wolf, Thomas
T1 - Hyperdeterminants as integrable discrete systems
N2 - 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.
T3 - ZIB-Report - 09-17
KW - hyper determinants
KW - integrable systems
KW - discrete equations
KW - large polynomial systems
KW - computer algebra
KW - Form
KW - Reduce
KW - Singular
Y1 - 2009
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1129
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-11292
SN - 1438-0064
ER -