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Hyperdeterminants as integrable discrete systems

Please always quote using this URN: urn:nbn:de:0297-zib-11292
  • 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.

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Author:Sergey Tsarev, Thomas Wolf
Document Type:ZIB-Report
Tag:Form; Reduce; Singular; computer algebra; discrete equations; hyper determinants; integrable systems; large polynomial systems
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52-04 Explicit machine computation and programs (not the theory of computation or programming)
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C99 None of the above, but in this section
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Ik Integrable systems
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.70.-c Computational techniques; simulations (for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics) / 02.70.Wz Symbolic computation (computer algebra)
Date of first Publication:2009/05/13
Series (Serial Number):ZIB-Report (09-17)
ArXiv Id:http://arxiv.org/abs/0903.3864
Published in:Appeared in: J. Phys. A: Math. Theor., 42 (2009), 454023, 9 pages
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