The argument shift method and maximal commutative subalgebras of Poisson algebras

By Dmitri I. Panyushev, Oksana Yakimova. 2007

49 citations recorded by the source corpus.

Let $S$ be the symmetric algebra of an algebraic Lie algebra. We provide a sufficient condition for the maximality of Poisson commutative subalgebras of $S$ obtained by the argument shift method.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fa45751c72b56c9861be6e52380684569a5a798

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Citations in the corpus

• Polynomiality of invariants, unimodularity and adapted pairs (2010, background): “Subsection 3.5). Again Panyushev and Yakimova [ 32 ] have shown that this rst condition may be weakened to just the requirement that codima sing 3; but that codima sing 2 does not generally suce (see also Subsection 8.3 for a particularly trivial example).”