Extensions of Algebraic Groups
| dc.creator | Kumar, S. | |
| dc.creator | Neeb, K. -H. | |
| dc.date | 2004-02-27 | |
| dc.date.accessioned | 2026-07-07T05:05:47Z | |
| dc.date.available | 2026-07-07T05:05:47Z | |
| dc.description | Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic group extensions of $G$ by $A$ in terms of a short exact sequence relating the ext-group to a relative second Lie algebra cohomology space and the fundamental group of the commutator group. Our second main result is an analog of the Van-Est Theorem for algebraic group cohomology, saying that for an algebraic $G$ module $\a$ and $p \geq 0$ the algebraic group cohomology $H^p_{alg}(G,\a)$ is given by the relative cohomology of the Lie algebra $\g$ with respect to the Lie algebra of a maximal reductive subgroup. | |
| dc.identifier | https://arxiv.org/abs/math/0402453 | |
| dc.identifier | http://arxiv.org/abs/math/0402453 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70299 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 20G12 (prim), 20G10 (sec) | |
| dc.title | Extensions of Algebraic Groups | |
| dc.type | text |