Observable subgroups of algebraic monoids
| dc.creator | Renner, Lex | |
| dc.creator | Rittatore, Alvaro | |
| dc.date | 2009-02-12 | |
| dc.date.accessioned | 2026-07-07T12:41:03Z | |
| dc.date.available | 2026-07-07T12:41:03Z | |
| dc.description | A closed subgroup H of the affine, algebraic group G is called observable if G/H is a quasi-affine algebraic variety. In this paper we define the notion of an observable subgroup of the affine, algebraic monoid M. We prove that a subgroup H of G is observable in M if and only if H is closed in M and there are "enough" H-semiinvariant functions in K[M]. We show also that a closed, normal subgroup H of G (the unit group of M) is observable in M if and only if it is closed in M. In such a case there exists a determinant $χ: M \to K$ such that $H\subset ker(χ)$. As an application, we show that in this case the affinized quotient $M/_{aff} H$ of M by H is an affine algebraic monoid scheme with unit group G/H. | |
| dc.description | 20 pages, uses elsarticle.cls (included for compatibility) | |
| dc.identifier | https://arxiv.org/abs/0902.2207 | |
| dc.identifier | http://arxiv.org/abs/0902.2207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219639 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L30, 20M99 | |
| dc.title | Observable subgroups of algebraic monoids | |
| dc.type | text |