Geometry of translations of invariants on semisimple Lie algebras
Journal Article
·
· Sbornik. Mathematics
- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
Each orbit of the coadjoint representation of a semisimple Lie algebra can be equipped with a complete commutative family of polynomials; this family was obtained by the argument-translation method in papers of Mishchenko and Fomenko. This commutative family and the corresponding Euler's equations play an important role in the theory of finite-dimensional integrable systems. These Euler's equations admit a natural Lax representation with spectral parameter. It is proved in the paper that the discriminant of the spectral curve coincides completely with the bifurcation diagram of the moment map for the algebra sl(n,C). The maximal degeneracy points of the moment map are described for compact semisimple Lie algebras in terms of the root structure. It is also proved that the set of regular points of the moment map is connected, and the inverse image of each regular point consists of precisely one Liouville torus.
- OSTI ID:
- 21208362
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 194; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
Similar Records
Uniqueness of liftings of maximal commutative subalgebras of the Poisson-Lie algebra to the enveloping algebra
Invariants of Lie algebras representable as semidirect sums with a commutative ideal
Integrability of soluble Lie algebras
Journal Article
·
Sun Aug 31 00:00:00 EDT 2003
· Sbornik. Mathematics
·
OSTI ID:21208337
Invariants of Lie algebras representable as semidirect sums with a commutative ideal
Journal Article
·
Mon Aug 31 00:00:00 EDT 2009
· Sbornik. Mathematics
·
OSTI ID:21301529
Integrability of soluble Lie algebras
Journal Article
·
Wed Jun 30 00:00:00 EDT 1999
· Sbornik. Mathematics
·
OSTI ID:21202861