2005/09/14 by Jean-Yves Charbonnel, Charbonnel, Jean-Yves
Mathematics · #14A10 #18G05 #18G10 #22E46 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT #msc:14A10 #msc:18G05 #msc:18G10 #msc:22E46
paper · pdf · doi:10.48550/arxiv.math/0509303
9 pages in french
arxiv created 2005/09/14 · openalex publication_date 2005/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \goth g be a finite dimensional complex reductive Lie algebra and \dv .. an invariant non degenerated bilinear form on \goth g× \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)↦ \dv v[x,y] on \goth g× \goth g. Then the complex C\bullet(\goth g) has no homology in degree strictly bigger than \rk \goth g.