The argument shift method and maximal commutative subalgebras of Poisson algebras
作者： Dmitri I. Panyushev , Oksana S. Yakimova
DOI: 10.4310/MRL.2008.V15.N2.A3
关键词: Mathematics 、 Algebra representation 、 Pure mathematics 、 Symmetric algebra 、 Poisson algebra 、 Graded Lie algebra 、 Division algebra 、 Cellular algebra 、 Lie conformal algebra 、 Subalgebra 、 Discrete mathematics 、 General Mathematics
摘要: Let $S$ be the symmetric algebra of an algebraic Lie algebra. We provide a sufficient condition for maximality Poisson commutative subalgebras obtained by argument shift method.
unirioja.es
intlpress.com 
sci-hub.st 参考文章(11)
Dmitri I. Panyushev, Semi-direct products of Lie algebras, their invariants and representations ,(2005)
Bertram Kostant, Nolan Wallach, Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II arXiv: Symplectic Geometry. pp. 319- 364 ,(2006) , 10.1007/0-8176-4467-9_10
B. Kostant, S. Rallis, Orbits and Representations Associated with Symmetric Spaces American Journal of Mathematics. ,vol. 93, pp. 753- ,(1971) , 10.2307/2373470
D. Panyushev, A. Premet, O. Yakimova, On symmetric invariants of centralisers in reductive Lie algebras Journal of Algebra. ,vol. 313, pp. 343- 391 ,(2007) , 10.1016/J.JALGEBRA.2006.12.026
Serge Ovsienko, Strongly nilpotent matrices and Gelfand–Zetlin modules Linear Algebra and its Applications. ,vol. 365, pp. 349- 367 ,(2003) , 10.1016/S0024-3795(02)00675-4
A A Tarasov, The maximality of certain commutative subalgebras in the Poisson algebra of a semisimple Lie algebra Russian Mathematical Surveys. ,vol. 57, pp. 1013- 1014 ,(2002) , 10.1070/RM2002V057N05ABEH000567
Dmitri I. Panyushev, Semi-Direct Products of Lie Algebras and their Invariants Publications of the Research Institute for Mathematical Sciences. ,vol. 43, pp. 1199- 1257 ,(2007) , 10.2977/PRIMS/1201012386
A. Joseph, P. Lamprou, Maximal Poisson Commutative subalgebras for truncated parabolic subalgebras of maximal index in sln Transformation Groups. ,vol. 12, pp. 549- 571 ,(2007) , 10.1007/S00031-006-0054-Z
Dmitri I. Panyushev, On the coadjoint representation of Z2 -contractions of reductive Lie algebras Advances in Mathematics. ,vol. 213, pp. 380- 404 ,(2007) , 10.1016/J.AIM.2006.12.011
Friedrich Knop, �ber die Glattheit von Quotientenabbildungen Manuscripta Mathematica. ,vol. 56, pp. 419- 427 ,(1986) , 10.1007/BF01168503