Kontsevich graphs act on Nambu–Poisson brackets, I. New identities for Jacobian determinants
Year: 2024
Type: conference-paper
Abstract: Nambu-determinant brackets on ℝ d ∋ x = (x 1, …, x d ), {f, g} d (x) = ϱ(x) · det (∂(f, g, a 1, …, a d−2) / ∂(x 1, …, x d )), with a i ∈ C ∞ (ℝ d ) and ϱ · ∂ x ∈ X d ( R d ) , are a class of degenerate (rank ⩽ 2) Poisson structures with (non)linear coefficients, e.g., polynomials of arbitrarily high degree. With ‘good’ cocycles in the graph complex, Kontsevich associated universal – for all Poisson bi-vectors P on affine ℝ aff d – elements P ˙ = Q γ ( [ P ] ) ∈ H P 2 ( ℝ aff d ) in the Lichnerowicz–Poisson second cohomology groups; we note that known graph cocycles γ preserve the Nambu–Poisson class {P (ϱ, [a]), and we express, directly from γ, the evolution ϱ ˙ , a ˙ that induces P ˙ . Over all d ⩾ 2 at once, there is no ‘universal’ mechanism for the bi-vector cocycles Q d γ to be trivial,
Institution: University of Groningen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405241027