# Symmetric Jacobians

Open Mathematics (2014)

- Volume: 12, Issue: 6, page 787-800
- ISSN: 2391-5455

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topMichiel Bondt. "Symmetric Jacobians." Open Mathematics 12.6 (2014): 787-800. <http://eudml.org/doc/269312>.

@article{MichielBondt2014,

abstract = {This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps. For instance, we show that it suffices to prove the Jacobian conjecture for polynomial maps x + H over ℂ such that satisfies all symmetries of the square, where H is homogeneous of arbitrary degree d ≥ 3.},

author = {Michiel Bondt},

journal = {Open Mathematics},

keywords = {Jacobian Conjecture; (Anti)symmetric Jacobian matrix; symmetry; anti-symmetry},

language = {eng},

number = {6},

pages = {787-800},

title = {Symmetric Jacobians},

url = {http://eudml.org/doc/269312},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Michiel Bondt

TI - Symmetric Jacobians

JO - Open Mathematics

PY - 2014

VL - 12

IS - 6

SP - 787

EP - 800

AB - This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps. For instance, we show that it suffices to prove the Jacobian conjecture for polynomial maps x + H over ℂ such that satisfies all symmetries of the square, where H is homogeneous of arbitrary degree d ≥ 3.

LA - eng

KW - Jacobian Conjecture; (Anti)symmetric Jacobian matrix; symmetry; anti-symmetry

UR - http://eudml.org/doc/269312

ER -

## References

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- [8] Druzkowski L.M., The Jacobian conjecture: symmetric reduction and solution in the symmetric cubic linear case, Ann. Polon. Math., 2005, 87, 83–92 http://dx.doi.org/10.4064/ap87-0-7 Zbl1098.14047
- [9] van den Essen A., Polynomial Automorphisms and the Jacobian Conjecture, Progr. Math., 190, Birkhäuser, Basel, 2000 Zbl0962.14037
- [10] van den Essen A.R.P., Hubbers E., A new class of invertible polynomial maps, J. Algebra, 1997, 187(1), 214–226 http://dx.doi.org/10.1006/jabr.1997.6788 Zbl0941.14002
- [11] Gordan P., Nöther M., Ueber die algebraischen Formen, deren Hesse’sche Determinante identisch verschwindet, Math. Ann., 1876, 10(4), 547–568 http://dx.doi.org/10.1007/BF01442264 Zbl08.0064.05
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