\(n\)-Poisson and \(n\)-Sklyanin brackets
It was proved independently by many authors that \(n\)-Poisson brackets, locally, are Jacobians on some subset of variables. The author presents the proof of this theorem obtained him in [Vestn. Samar. Gos. Univ., Mat. Mekh. Fiz. Khim. Biol. 1996, No.2, 33--41 (1996; Zbl 0986.37048)]. He also considers the notion of \(n\)-Sklyanin brackets and gives without proof a theorem on their symplectic leaves and Casimir functions.
scientific article; zbMATH DE number 1777798