The Kontsevich tetrahedral flow revisited

作者：Bouisaghouane A; Buring R; Kiselev A^*

来源：Journal of Geometry and Physics, 2017, 119: 272-285.

DOI：10.1016/j.geomphys.2017.04.014

• Poisson bracket
• Affine manifold
• Graph complex
• Tetrahedral flow
• Poisson cohomology

We prove that the Kontsevich tetrahedral flow (P) over circle = Q(a:b)(P), the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector P on an affine real Poisson manifold N-n, does infinitesimally preserve the space of Poisson bi-vectors on N-n if and only if the two monomials in Q(a:b)(P) are balanced by the ratio a : b = 1 : 6. The proof is explicit; it is written in the language of Kontsevich graphs.

• 出版日期2017-9