Hyperdeterminants as integrable discrete systems
Exactly Solvable and Integrable Systems
2015-05-13 v2
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 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 2x2x2x2-hyperdeterminant.
Cite
@article{arxiv.0903.3864,
title = {Hyperdeterminants as integrable discrete systems},
author = {Sergey P. Tsarev and Thomas Wolf},
journal= {arXiv preprint arXiv:0903.3864},
year = {2015}
}
Comments
Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstract