@misc{TsarevWolf, author = {Tsarev, Sergey and Wolf, Thomas}, title = {Hyperdeterminants as integrable discrete systems}, issn = {1438-0064}, doi = {10.1088/1751-8113/42/45/454023}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11292}, number = {09-17}, abstract = {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.}, language = {en} }