$L_\infty$-interpretation of a classification of deformations of Poisson structures in dimension three

zbMATH Open1287.17044arXiv0904.0945MaRDI QIDQ3060999

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Publication date: 13 December 2010

Abstract: We give an $L_{i}nfty$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again the explicit formulas for all the formal deformations of these Poisson structures, together with a classification in the generic case, by constructing a suitable quasi-isomorphism between two $L_{i}nfty$-algebras, which are associated to these Poisson structures.

Full work available at URL: https://arxiv.org/abs/0904.0945

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