The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-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 the isomorphism classes of...

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Detalles Bibliográficos
Autores: Plaza Martín, Francisco José, Tejero Prieto, Tomás Carlos
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:10366/159334
Acceso en línea:http://hdl.handle.net/10366/159334
Access Level:acceso abierto
Palabra clave:Torsion free sl(2)-modules
Rational sl(2)-modules
Grothendieck group Picard group
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spelling The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modulesPlaza Martín, Francisco JoséTejero Prieto, Tomás CarlosTorsion free sl(2)-modulesRational sl(2)-modulesGrothendieck group Picard group[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 the isomorphism 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.Springer202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/159334reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)Inglésinfo:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1593342026-06-07T06:28:51Z
dc.title.none.fl_str_mv The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
title The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
spellingShingle The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
Plaza Martín, Francisco José
Torsion free sl(2)-modules
Rational sl(2)-modules
Grothendieck group Picard group
title_short The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
title_full The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
title_fullStr The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
title_full_unstemmed The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
title_sort The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
dc.creator.none.fl_str_mv Plaza Martín, Francisco José
Tejero Prieto, Tomás Carlos
author Plaza Martín, Francisco José
author_facet Plaza Martín, Francisco José
Tejero Prieto, Tomás Carlos
author_role author
author2 Tejero Prieto, Tomás Carlos
author2_role author
dc.subject.none.fl_str_mv Torsion free sl(2)-modules
Rational sl(2)-modules
Grothendieck group Picard group
topic Torsion free sl(2)-modules
Rational sl(2)-modules
Grothendieck group Picard group
description [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 the isomorphism 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.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/159334
url http://hdl.handle.net/10366/159334
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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