The Grothendieck and Picard groups of finite rank torsion free {sl}(2)-modules
[EN] The classification problem for simple sl(2)-modules leads in a natural way to the study of the category of finite rank torsion free sl(2)-modules and its subcategory of rational sl(2)-modules. We prove that the rationalization functor induces an identification between theisomorphism classes of...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/150941 |
| Acceso en línea: | http://hdl.handle.net/10366/150941 |
| Access Level: | acceso abierto |
| Palabra clave: | Torsion free sl(2)-modules Rational sl(2)-modules Grothendieck group Picard group 1210 Topología 1201.09 Álgebra de Lie |
| Sumario: | [EN] The classification problem for simple sl(2)-modules leads in a natural way to the study of the category of finite rank torsion free sl(2)-modules and its subcategory of rational sl(2)-modules. We prove that the rationalization functor induces an identification between theisomorphism classes of simple modules of these categories. This raises the question of what is the precise relationship between other invariants associated with them. We give a complete solution to this problem for the Grothendieck and Picard groups, obtaining along the way several new results regarding these categories that are interesting in their own right. |
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