Geodesic
A K\"ahler structure of the triplectic geometry
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 355-372

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We study the geometry of the triplectic quantization of gauge theories. We show that the triplectic geometry is determined by the geometry of a Kähler manifold $\mathcal N$ endowed with a pair of transversal polarizations. The antibrackets can be brought to the canonical form if and only if $\mathcal N$ admits a flat symmetric connection that is compatible with the complex structure and the polarizations. 
@article{TMF_2000_124_3_a0,
     author = {M. A. Grigoriev and A. M. Semikhatov},
     title = {A {K\"ahler} structure of the triplectic geometry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--372},
     publisher = {mathdoc},
     volume = {124},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/}
}
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M. A. Grigoriev; A. M. Semikhatov. A K\"ahler structure of the triplectic geometry. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 355-372. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a0/