On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras

Details On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras

2006-10-16

arxiv.org/abs/math/0610493v1

Mathematics

Representation Theory

25 pages, 3 tables

Scientific paper

We study the coadjoint representation of contractions of reductive Lie algebras associated with symmetric decompositions. Let $\frak g=\frak g_0\oplus \frak g_1$ be a symmetric decomposition of a reductive Lie algebra $\frak g$. Then the semi-direct product of $\frak g_0$ and the $\frak g_0$-module $\frak g_1$ is a contraction of $\frak g$. 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.

Affiliated with

Also associated with

No associations

Rating

On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-244917