# Publication: Hyperdeterminants as integrable discrete systems

All || By Area || By YearTitle | 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 |

Link | http://lie.math.brocku.ca/twolf/papers/Tsarev-Wolf-hyperdets-JPhysA2009.pdf |

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 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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