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Vinberg, Ernest B. and Yakimova, Oksana S. (2019). Complete families of commuting functions for coisotropic Hamiltonian actions. Adv. Math., 348. S. 523 - 541. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2082

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Abstract

Let G be an algebraic group defined over a field F of characteristic zero with g = Lie G. The dual space g* equipped with the Lie Poisson bracket is a Poisson variety and each irreducible G-invariant subvariety X subset of g* carries the induced Poisson structure. We prove that there is a set {f(1),..., f(1)} subset of F [X] of algebraically independent polynomial functions, which pairwise commute with respect to the Poisson bracket, such that l = (dim X + tr.degF(X)(G))/2. We also discuss several applications of this result to complete integrability of Hamiltonian systems on symplectic Hamiltonian G-varieties of corank zero and 2. (C) 2019 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Vinberg, Ernest B. UNSPECIFIED UNSPECIFIED UNSPECIFIED Yakimova, Oksana S. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-147848
DOI:	10.1016/j.aim.2019.03.024
Journal or Publication Title:	Adv. Math.
Volume:	348
Page Range:	S. 523 - 541
Date:	2019
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2082
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/14784