Semi-direct products of Lie algebras and their invariants

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dc.creatorPanyushev, Dmitri I.
dc.date2005-06-28
dc.date2007-10-17
dc.date.accessioned2026-07-07T08:36:43Z
dc.date.available2026-07-07T08:36:43Z
dc.descriptionThe goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the existence of generic stabilisers and generic isotropy groups for finite-dimensional representations; structure of the fields and algebras of invariants; quotient morphisms and structure of their fibres. One of the main tools for obtaining non-reductive Lie algebras is the semi-direct product construction. We observe that there are surprisingly many non-reductive Lie algebras whose adjoint representation has a polynomial algebra of invariants. We extend results of Takiff, Geoffriau, Rais-Tauvel, and Levasseur-Stafford concerning Takiff Lie algebras to a wider class of semi-direct products. This includes $Z_2$-contractions of simple Lie algebras and generalised Takiff algebras.
dc.description49 pages, title changed, section 11 is shortened, numerous minor corrections; accepted version, to appear in Publ. RIMS 43(2007)
dc.identifierhttps://arxiv.org/abs/math/0506579
dc.identifierhttp://arxiv.org/abs/math/0506579
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140158
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.titleSemi-direct products of Lie algebras and their invariants
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