Year: 2024
Type: conference-paper
Abstract: Kontsevich constructed a map between ‘good’ graph cocycles γ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz–Poisson cohomology. For the tetrahedral graph cocycle γ 3 and for the class of Nambu-determinant Poisson bivectors P over ℝ2, ℝ3 and ℝ4, we know the fact of trivialization, P ˙ = 〚 P , X → dim γ3 〛 , by using dimension-dependent vector fields X → dim γ3 expressed by Kontsevich (micro-)graphs. We establish that these trivializing vector fields X → dim γ3 are unique modulo Hamiltonian vector fields X → H = d P ( H ) = 〚 P , H 〛 , where d P is the Lichnerowicz–Poisson differential and where the Hamiltonians H are also represented by Kontsevich (micro-)graphs. However, we find that the choice of Kontsevich (micro-)graphs to represent the aforementioned multivectors is not unique.
Authors: F M Schipper, M S Jagoe Brown, A V Kiselev
Institution: University of Groningen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Rijksuniversiteit Groningen
OpenAlex ID: W4405240976