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@article{962359,
author = {Batalin, Igor and Bering Larsen, Klaus},
article_location = {USA},
article_number = {12},
doi = {http://dx.doi.org/10.1063/1.4759501},
keywords = {Poisson Bracket; Antibracket; Sp(2)-Symmetric Quantization; Darboux Theorem; Poincare Lemma.},
language = {eng},
issn = {0022-2488},
journal = {Journal of Mathematical Physics},
title = {A triplectic bi-Darboux theorem and para-hypercomplex geometry},
url = {http://dx.doi.org/10.1063/1.4759501},
volume = {53},
year = {2012}
}
TY - JOUR
ID - 962359
AU - Batalin, Igor - Bering Larsen, Klaus
PY - 2012
TI - A triplectic bi-Darboux theorem and para-hypercomplex geometry
JF - Journal of Mathematical Physics
VL - 53
IS - 12
SP - 1-25
EP - 1-25
PB - American Institute of Physics
SN - 00222488
KW - Poisson Bracket
KW - Antibracket
KW - Sp(2)-Symmetric Quantization
KW - Darboux Theorem
KW - Poincare Lemma.
UR - http://dx.doi.org/10.1063/1.4759501
N2 - We provide necessary and sufficient conditions for a bi-Darboux Theorem on triplectic manifolds. Here triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the manifold dimension. By definition bi-Darboux coordinates are common Darboux coordinates for two Poisson brackets. We discuss both the Grassmann-even and the Grassmann-odd Poisson bracket case. Odd triplectic manifolds are, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence between triplectic manifolds and para-hypercomplex manifolds. Existence of bi-Darboux coordinates on the triplectic side of the correspondence translates into a flat Obata connection on the para-hypercomplex side.
ER -
BATALIN, Igor a Klaus BERING LARSEN. A triplectic bi-Darboux theorem and para-hypercomplex geometry. \textit{Journal of Mathematical Physics}. USA: American Institute of Physics, 2012, roč.~53, č.~12, s.~1-25. ISSN~0022-2488. Dostupné z: https://dx.doi.org/10.1063/1.4759501.
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