Complexe canonique d'une algèbre de Lie réductive

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dc.creatorCharbonnel, Jean-Yves
dc.date2005-09-14
dc.date.accessioned2026-07-07T05:23:11Z
dc.date.available2026-07-07T05:23:11Z
dc.descriptionLet ${\goth g}$ be a finite dimensional complex reductive Lie algebra and $\dv ..$ an invariant non degenerated bilinear form on ${\goth g}\times {\goth g}$ which extends the Killing form of $[{\goth g},{\goth g}]$. We define the homology complex $C_{\bullet}({\goth g})$. Its space is the algebra $\tk {\Bbb C}{\e Sg}\tk {\Bbb C}{\e Sg}\ex {}{\goth g}$ where $\e Sg$ and $\ex {}{\goth g}$ are the symmetric and exterior algebras of ${\goth g}$. The differential of $C_{\bullet}({\goth g})$ is the $\tk {\Bbb C}{\e Sg}\e Sg$-derivation which associates to the element $v$ of ${\goth g}$ the function $(x,y)\mapsto \dv v{[x,y]}$ on ${\goth g}\times {\goth g}$. Then the complex $C_{\bullet}({\goth g})$ has no homology in degree strictly bigger than $\rk {\goth g}$.
dc.description9 pages in french
dc.identifierhttps://arxiv.org/abs/math/0509303
dc.identifierhttp://arxiv.org/abs/math/0509303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76333
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subject14A10, 18G05, 18G10, 22E46
dc.titleComplexe canonique d'une algèbre de Lie réductive
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