On the coadjoint representation of Z2 -contractions of reductive Lie algebras
By Dmitri I. Panyushev. 2007
53 citations recorded by the source corpus.
Abstract We study the coadjoint representation of contractions of reductive Lie algebras associated with symmetric decompositions. Let g = g 0 ⊕ g 1 be a symmetric decomposition of a reductive Lie algebra g . Then the semi-direct product of g 0 and the g 0 -module g 1 is a contraction of g . We conjecture that these contractions have many properties in common with reductive Lie algebras. In particular, it is proved that in many cases the algebra of invariants is polynomial. We also discuss the so-called “codim-2 property” for coadjoint representations and its relationship with the structure of algebra of invariants.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7a732990b18f09e6de800666c73720d434afc42a
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In Algebra and Number Theory
- Doron Shafrir
- Anthony Joseph
- Oksana Yakimova
- Dmitri I. Panyushev
- Paul Blain Levy
- Mark Reeder
- E. Sommers
In Geometry and Topology
- Doron Shafrir
- Anthony Joseph
- Oksana Yakimova
- Dmitri I. Panyushev
- Paul Blain Levy
- Mark Reeder
- E. Sommers
In Mathematical Physics
Citations in the corpus
- Polynomiality of invariants, unimodularity and adapted pairs (2010, result): “This section renes the results of [36] which were in turn inspired by the results in [ 30 ], [31].”
- The argument shift method and maximal commutative subalgebras of Poisson algebras (2007, background): “ctions associatedwiththefollowingsymmetricpairs(g,g0): (sl2n,sp2 n);(sln+1,gl ),n > 2;(son,son−1); (E6,F4); (F4,B4). However, the complete list is not known yet. For items 2,3, and 5, it is shownin[11]thatZ(q)ispolynomialandthesumofdegreesofthefreegenerators equals b(q). Hence Theorem 3.2 applies”