2012/07/25 by Jon F. Carlson, Carlson, Jon F., Eric M. Friedlander +3 · 2 citations
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1207.5898
The paper has been split into two at the request of the referee, the first part has the same title as the older combined version
arxiv created 2014/09/24 · arxiv updated 2014/09/25
We initiate the investigation of the projective variety E(r,g) of elementary subalgebras of dimension r of a (p-restricted) Lie algebra g for some r > 0 and demonstrate that this variety encodes considerable information about the representations of g. For various choices of g and r, we identify the geometric structure of E(r,g). We show that special classes of (restricted) representations of g lead to algebraic vector bundles on E(r,g). For g = Lie(G) the Lie algebra of an algebraic group G, rational representations of G enable us to realize familiar algebraic vector bundles on G-orbits of E(r, g).