Star products modulo skew-symmetric biderivations

Details Star products modulo skew-symmetric biderivations Star products modulo skew-symmetric biderivations

2011-03-27

arxiv.org/abs/1103.5213v2

Physics

Mathematical Physics

8 pages; minor corrections

Scientific paper

We obtain the expression, which defines star products on Poisson manifolds up to a family of skew-symmetric biderivations. To this end, we split the Maurer-Cartan equation into a pair of complementary equations and find the general solution to one of them. Another equation describes the part of deformation which depends only on skew-symmetric biderivations. The solution possesses a graphical representation in terms of diagrams. In the case of linear Poisson structures the formula is exact.

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