Nearly Frobenius structures in some families of algebras.
Resumen:
In this article we continue with the study started in [2] of nearly Frobenius structures in some representative families of finite dimensional algebras, as radical square zero algebras, string algebras and toupie algebras. We prove that such radical square zero algebras with at least one path of length two are nearly Frobenius. As for the string algebras, those who are not gentle can be endowed with at least one non-trivial nearly Frobenius structure. Finally, in the case of toupie algebras, we prove that the existence of monomial relations is a sufficient condition to have non-trivial nearly Frobenius structures. Using the technics developed for the previous families of algebras we prove sufficient conditions for the existence of non-trivial Frobenius structures in quotients of path algebras in general.
| 2019 | |
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Nearly Frobenius String algebra Radical square zero algebra |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47556 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1877555087295905792 |
|---|---|
| author | Artenstein, Dalia |
| author2 | González, Ana Mata, Gustavo |
| author2_role | author author |
| author_facet | Artenstein, Dalia González, Ana Mata, Gustavo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Artenstein Dalia, Universidad de la República (Uruguay). Facultad de Ingeniería. González Ana, Universidad de la República (Uruguay). Facultad de Ingeniería. Mata Gustavo, Universidad de la República (Uruguay). Facultad de Ingeniería. |
| dc.creator.none.fl_str_mv | Artenstein, Dalia González, Ana Mata, Gustavo |
| dc.date.accessioned.none.fl_str_mv | 2024-12-16T17:48:45Z |
| dc.date.available.none.fl_str_mv | 2024-12-16T17:48:45Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | In this article we continue with the study started in [2] of nearly Frobenius structures in some representative families of finite dimensional algebras, as radical square zero algebras, string algebras and toupie algebras. We prove that such radical square zero algebras with at least one path of length two are nearly Frobenius. As for the string algebras, those who are not gentle can be endowed with at least one non-trivial nearly Frobenius structure. Finally, in the case of toupie algebras, we prove that the existence of monomial relations is a sufficient condition to have non-trivial nearly Frobenius structures. Using the technics developed for the previous families of algebras we prove sufficient conditions for the existence of non-trivial Frobenius structures in quotients of path algebras in general. |
| dc.description.es.fl_txt_mv | También publicado en São Paulo Journal of Mathematical Sciences, vol. 14, 2020, pp. 165-184. DOI : 10.1007/s40863-019-00158-z. |
| dc.format.extent.es.fl_str_mv | 17 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Artenstein, D., González, A. y Mata, G. Nearly Frobenius structures in some families of algebras. [Preprint]. Publicado en: Mathematics. Rings and Algebras (math.RA), 2019, pp. 1-17. arXiv:1705.10222v3. DOI: 10.48550/arXiv.1705.10222. |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/47556 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.none.fl_str_mv | Mathematics. Rings and Algebras (math.RA), arXiv:1705.10222v3, mar. 2019, pp. 1-17. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Nearly Frobenius String algebra Radical square zero algebra |
| dc.title.none.fl_str_mv | Nearly Frobenius structures in some families of algebras. |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | También publicado en São Paulo Journal of Mathematical Sciences, vol. 14, 2020, pp. 165-184. DOI : 10.1007/s40863-019-00158-z. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_eba36c8b91de0d8bfc7e8d3a4dcf2faa |
| identifier_str_mv | Artenstein, D., González, A. y Mata, G. Nearly Frobenius structures in some families of algebras. [Preprint]. Publicado en: Mathematics. Rings and Algebras (math.RA), 2019, pp. 1-17. arXiv:1705.10222v3. DOI: 10.48550/arXiv.1705.10222. |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/47556 |
| publishDate | 2019 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Artenstein Dalia, Universidad de la República (Uruguay). Facultad de Ingeniería.González Ana, Universidad de la República (Uruguay). Facultad de Ingeniería.Mata Gustavo, Universidad de la República (Uruguay). Facultad de Ingeniería.2024-12-16T17:48:45Z2024-12-16T17:48:45Z2019Artenstein, D., González, A. y Mata, G. Nearly Frobenius structures in some families of algebras. [Preprint]. Publicado en: Mathematics. Rings and Algebras (math.RA), 2019, pp. 1-17. arXiv:1705.10222v3. DOI: 10.48550/arXiv.1705.10222.https://hdl.handle.net/20.500.12008/47556También publicado en São Paulo Journal of Mathematical Sciences, vol. 14, 2020, pp. 165-184. DOI : 10.1007/s40863-019-00158-z.In this article we continue with the study started in [2] of nearly Frobenius structures in some representative families of finite dimensional algebras, as radical square zero algebras, string algebras and toupie algebras. We prove that such radical square zero algebras with at least one path of length two are nearly Frobenius. As for the string algebras, those who are not gentle can be endowed with at least one non-trivial nearly Frobenius structure. Finally, in the case of toupie algebras, we prove that the existence of monomial relations is a sufficient condition to have non-trivial nearly Frobenius structures. Using the technics developed for the previous families of algebras we prove sufficient conditions for the existence of non-trivial Frobenius structures in quotients of path algebras in general.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2024-12-14T00:26:24Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) AGM19.pdf: 221823 bytes, checksum: f110ce9022acc13809df121434c231ec (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2024-12-16T15:51:55Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) AGM19.pdf: 221823 bytes, checksum: f110ce9022acc13809df121434c231ec (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-12-16T17:48:45Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) AGM19.pdf: 221823 bytes, checksum: f110ce9022acc13809df121434c231ec (MD5) Previous issue date: 201917 p.application/pdfenengarXivMathematics. Rings and Algebras (math.RA), arXiv:1705.10222v3, mar. 2019, pp. 1-17.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Nearly FrobeniusString algebraRadical square zero algebraNearly Frobenius structures in some families of algebras.Preprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaArtenstein, DaliaGonzález, AnaMata, GustavoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/47556/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/47556/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Nearly Frobenius structures in some families of algebras. Artenstein, Dalia Nearly Frobenius String algebra Radical square zero algebra |
| status_str | submittedVersion |
| title | Nearly Frobenius structures in some families of algebras. |
| title_full | Nearly Frobenius structures in some families of algebras. |
| title_fullStr | Nearly Frobenius structures in some families of algebras. |
| title_full_unstemmed | Nearly Frobenius structures in some families of algebras. |
| title_short | Nearly Frobenius structures in some families of algebras. |
| title_sort | Nearly Frobenius structures in some families of algebras. |
| topic | Nearly Frobenius String algebra Radical square zero algebra |
| url | https://hdl.handle.net/20.500.12008/47556 |
