Oh the maximality of sp(l) in spn(k)
Let k be the quotient field of a Dedekind domain O, (k ≠ 0) and let G = Spn(k) be the Symplectic Group over k. G acts on the 2n -dimensional vector space V.Let L be a lattice in V, and let Sp(L) be the stabilizer of L in Spn(k). Our purpose is to investigate whether or not there exists a subgroup of...
- Autores:
-
Allan, Nelo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1970
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42156
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42156
http://bdigital.unal.edu.co/32253/
- Palabra clave:
- 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Quotient field
dedekind domain
symplectic group
finite index
finitely
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Let k be the quotient field of a Dedekind domain O, (k ≠ 0) and let G = Spn(k) be the Symplectic Group over k. G acts on the 2n -dimensional vector space V.Let L be a lattice in V, and let Sp(L) be the stabilizer of L in Spn(k). Our purpose is to investigate whether or not there exists a subgroup of Spn(k) which contains Sp(L) as a subgroup of finite index. Although in several points we need only weaker assumptions, to describe our methods we shall assume that all residue class fields of k are finite. First of all we would like to point out th at the 0- module A(Sp(L),O) generated by Sp(L) in Mn(k). is an order, i.e., it is a subring which is a finitely generated 0-module and generates Mn(k) over k. |
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