Cartan subgroups and regular points of o‐minimal groups
| dc.contributor.author | Baro González, Elías | |
| dc.contributor.author | Berarducci, Alessandro | |
| dc.contributor.author | Otero, Margarita | |
| dc.date.accessioned | 2023-06-17T13:34:19Z | |
| dc.date.available | 2023-06-17T13:34:19Z | |
| dc.date.issued | 2019-10-01 | |
| dc.description.abstract | Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their Lie algebras which allow us to prove firstly, that every Cartan subalgebra of the Lie algebra of G is the Lie algebra of a definable subgroup – a Cartan subgroup of G –, and secondly, that the set of regular points of G – a dense subset of G – is formed by points which belong to a unique Cartan subgroup of G. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (España) | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (España) | |
| dc.description.sponsorship | Universidad Complutense de Madrid | |
| dc.description.sponsorship | MIUR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/57844 | |
| dc.identifier.doi | 10.1112/jlms.12216 | |
| dc.identifier.issn | 1469-7750 | |
| dc.identifier.officialurl | https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12216 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/13777 | |
| dc.journal.title | Journal of the London Mathematical Society | |
| dc.language.iso | eng | |
| dc.publisher | London Mathematical Society | |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-55565-P | |
| dc.relation.projectID | FECYT -- ESTRUCTURAS ALGEBRAICAS, ANALITICAS Y O-MINIMALES | |
| dc.relation.projectID | UCM (910444) | |
| dc.relation.projectID | PRIN 2012 ‘Logica, Modelli e Insiemi’ | |
| dc.relation.projectID | Progetto di Ricerca d'Ateneo 2015 ‘Connessioni fra dinamica olomorfa, teoria ergodica e logica matematica nei sistemi dinamici’. | |
| dc.relation.projectID | Università di Pisa. Grant Number: PRA 2015 Connessioni fra dinamica olomorfa, teoria ergodica e logica matematica nei sistemi dinamici | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 510.6 | |
| dc.subject.cdu | 164 | |
| dc.subject.keyword | Lógica simbólica y matemática | |
| dc.subject.keyword | Teoría de grupos | |
| dc.subject.keyword | Mathematical logic and foundations | |
| dc.subject.keyword | Group theory | |
| dc.subject.ucm | Matemáticas (Matemáticas) | |
| dc.subject.ucm | Grupos (Matemáticas) | |
| dc.subject.ucm | Lógica simbólica y matemática (Matemáticas) | |
| dc.subject.unesco | 12 Matemáticas | |
| dc.subject.unesco | 1102.14 Lógica Simbólica | |
| dc.title | Cartan subgroups and regular points of o‐minimal groups | |
| dc.type | journal article | |
| dcterms.references | 1. E. Baro, E. Jaligot and M. Otero, ‘ Commutators in groups definable in o‐minimal structures’, Proc. Amer. Math. Soc. 140 (2012) 3629– 3643. 2. E. Baro, E. Jaligot and M. Otero, ‘ Cartan subgroups of groups definable in o‐minimal structures’, J. Inst. Math. Jussieu 13 (2014) 849– 893. 3. A. Berarducci, M. Otero, Y. Peterzil and A. Pillay, ‘ A descending chain condition for groups definable in o‐minimal structures’, Ann. Pure Appl. Logic 134 (2005) 303– 313. 4. A. Borel, Linear algebraic groups, Graduate Texts in Mathematics 126 ( Springer, New York, 1991). 5. N. Bourbaki, Lie groups and Lie algebras, Chapters 7–9 ( Springer, Berlin, 2005). (Translated from the 1975 and 1982 French originals by Andrew Pressley.) 6. C. Chevalley, Théorie des groupes de Lie. Tome III. Théorèmes généraux sur les algèbres de Lie, Actualités Scientifiques et Industrielles 1226 ( Hermann & Cie, Paris, 1955). 7. A. Conversano, ‘ Maximal compact subgroups in the o‐minimal setting’, J. Math. Log. 13 (2013) 1350004. 8. M. J. Edmundo, ‘ Solvable groups definable in o‐minimal structures’, J. Pure Appl. Algebra 185 (2003) 103– 145. 9. M. J. Edmundo and M. Otero, ‘ Definably compact abelian groups’, J. Math. Log. 4 (2004) 163– 180. 10. O. Frécon, ‘ Linearity of groups definable in o‐minimal structures’, Selecta Math. (N.S.) 23 (2017) 1563– 1598. 11. G. P. Hochschild, Basic theory of algebraic groups and Lie algebras, Graduate Texts in Mathematics 75 ( Springer, New York, 1981). 12. K. H. Hofmann, ‘ Near‐Cartan algebras and groups’, Sem. Sophus Lie 2 (1992) 135– 151. 13. E. Hrushovski, Y. Peterzil and A. Pillay, ‘ Groups, measures, and the NIP’, J. Amer. Math. Soc. 21 (2008) 563– 596. 14. A. W. Knapp, Lie groups beyond an introduction, 2nd edn, Progress in Mathematics 140 ( Birkhäuser Boston, Boston, MA, 2002). 15. K.‐H. Neeb, ‘ On closedness and simple connectedness of adjoint and coadjoint orbits’, Manuscripta Math. 82 (1994) 51– 65. 16. K.‐H. Neeb, ‘ Weakly exponential Lie groups’, J. Algebra 179 (1996) 331– 361. 17. M. Otero, ‘ A survey on groups definable in o‐minimal structures’. Model theory with applications to algebra and analysis, vol. 2, London Mathematical Society Lecture Note Series 350 (eds Z. Chatzidakis, D. Macpherson, A. Pillay and A. Wilkie; Cambridge University Press, Cambridge, 2008) 177– 206. 18. Y. Peterzil, A. Pillay and S. Starchenko, ‘ Definably simple groups in o‐minimal structures’, Trans. Amer. Math. Soc. 352 (2000) 4397– 4419. 19. Y. Peterzil, A. Pillay and S. Starchenko, ‘ Linear groups definable in o‐minimal structures’, J. Algebra 247 (2002) 1– 23. 20. A. Pillay, ‘ On groups and fields definable in | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8695b08a-762f-4ef9-ad24-b6fe687ab7cd | |
| relation.isAuthorOfPublication.latestForDiscovery | 8695b08a-762f-4ef9-ad24-b6fe687ab7cd |
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