Non-decomposable Nambu brackets

Klaus Bering

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 4, page 211-232
  • ISSN: 0044-8753

Abstract

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It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.

How to cite

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Bering, Klaus. "Non-decomposable Nambu brackets." Archivum Mathematicum 051.4 (2015): 211-232. <http://eudml.org/doc/276245>.

@article{Bering2015,
abstract = {It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.},
author = {Bering, Klaus},
journal = {Archivum Mathematicum},
keywords = {Nambu bracket; Darboux Theorem; Moser trick; multisymplectic; presymplectic; Weinstein splitting principle},
language = {eng},
number = {4},
pages = {211-232},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Non-decomposable Nambu brackets},
url = {http://eudml.org/doc/276245},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Bering, Klaus
TI - Non-decomposable Nambu brackets
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 4
SP - 211
EP - 232
AB - It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.
LA - eng
KW - Nambu bracket; Darboux Theorem; Moser trick; multisymplectic; presymplectic; Weinstein splitting principle
UR - http://eudml.org/doc/276245
ER -

References

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