Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebras
Abstract
The Mischenko-Fomenko argument shift method allows to construct commutative subalgebras in the symmetric algebra $S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$. For a wide class of Lie algebras, these commutative subalgebras appear to be complete, i.e. they have maximal transcendence degree. However, for many algebras, Mischenko-Fomenko subalgebras are incomplete or even empty. In this case, we suggest a natural way how to extend Mischenko-Fomenko subalgebras, and give a completeness criterion for these extended subalgebras.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.3777
- arXiv:
- arXiv:1406.3777
- Bibcode:
- 2014arXiv1406.3777I
- Keywords:
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- Mathematics - Representation Theory