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

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dc.creatorPanyushev, Dmitri I.
dc.date2006-10-16
dc.date.accessioned2026-07-07T07:29:07Z
dc.date.available2026-07-07T07:29:07Z
dc.descriptionWe 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.
dc.description25 pages, 3 tables
dc.identifierhttps://arxiv.org/abs/math/0610493
dc.identifierhttp://arxiv.org/abs/math/0610493
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117983
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.titleOn the coadjoint representation of $\mathbb Z_2$-contractions of reductive Lie algebras
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