\(n\)-Poisson and \(n\)-Sklyanin brackets
type: Item
instance of: scholarly article
title: \(n\)-Poisson and \(n\)-Sklyanin brackets
zbMATH Open document ID: 1048.17002
DOI: 10.1023/A:1014953924173
author: A. N. Panov
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-09-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17A42
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 53D17
zbMATH DE Number: 1777798
zbMATH Keywords: \(n\)-Lie algebra
zbMATH Keywords: Filippov algebra
zbMATH Keywords: \(n\)-Poisson bracket
zbMATH Keywords: \(n\)-Sklyanin bracket
zbMATH Keywords: symplectic leaf
zbMATH Keywords: Casimir function
reviewed by: Alexandre P. Pojidaev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1777798