Strong equivalence of graded algebras
Resumen:
We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. As to a more general idempotent graded algebra B, we point out that the Cohen-Montgomery duality holds for B, and B is graded-equivalent to a global skew group algebra. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that any product partial group action α is globalizable up to Morita equivalence; if such a globalization β is minimal, then the skew group algebras by α and β are graded-equivalent; moreover, β is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras are stably isomorphic as graded algebra
| 2024 | |
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MORITA EQUIVALENCE RADED ALGEBRA PARTIAL ACTION SKEW GROUP RING SMASH PRODUCT |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/48378 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1877555101916200960 |
|---|---|
| author | Abadie, Fernando |
| author2 | Dokuchaev, Michael Exel, Ruy |
| author2_role | author author |
| author_facet | Abadie, Fernando Dokuchaev, Michael Exel, Ruy |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Abadie Fernando, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática Dokuchaev Michael Exel Ruy |
| dc.creator.none.fl_str_mv | Abadie, Fernando Dokuchaev, Michael Exel, Ruy |
| dc.date.accessioned.none.fl_str_mv | 2025-02-13T15:27:42Z |
| dc.date.available.none.fl_str_mv | 2025-02-13T15:27:42Z |
| dc.date.issued.none.fl_str_mv | 2024 |
| dc.description.abstract.none.fl_txt_mv | We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. As to a more general idempotent graded algebra B, we point out that the Cohen-Montgomery duality holds for B, and B is graded-equivalent to a global skew group algebra. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that any product partial group action α is globalizable up to Morita equivalence; if such a globalization β is minimal, then the skew group algebras by α and β are graded-equivalent; moreover, β is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras are stably isomorphic as graded algebra |
| dc.description.es.fl_txt_mv | Versión permitida preprint. Publicado también en: Journal of Algebra, 2024, 659(1): 818-858. DOI: 10.1016/j.jalgebra.2024.07.014 |
| dc.format.extent.es.fl_str_mv | 38 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Abadie, F, Dokuchaev, M y Exel, R. "Strong equivalence of graded algebras". [Preprint]. Publicado en: Mathematics (Rings and Algebras). 2024, arXiv.2201.03513, jul. 2024, pp.1-38. DOI: 10.48550/arXiv.2201.03513 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2201.03513 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/48378 |
| 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). arXiv:2201.03513, jul. 2024, pp.1-38 |
| 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.other.es.fl_str_mv | MORITA EQUIVALENCE RADED ALGEBRA PARTIAL ACTION SKEW GROUP RING SMASH PRODUCT |
| dc.title.none.fl_str_mv | Strong equivalence of graded 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 | Versión permitida preprint. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_70e4e855d805b89e1f6baaf77cf79756 |
| identifier_str_mv | Abadie, F, Dokuchaev, M y Exel, R. "Strong equivalence of graded algebras". [Preprint]. Publicado en: Mathematics (Rings and Algebras). 2024, arXiv.2201.03513, jul. 2024, pp.1-38. DOI: 10.48550/arXiv.2201.03513 10.48550/arXiv.2201.03513 |
| 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:20.500.12008/48378 |
| publishDate | 2024 |
| 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 | Abadie Fernando, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de MatemáticaDokuchaev MichaelExel Ruy2025-02-13T15:27:42Z2025-02-13T15:27:42Z2024Abadie, F, Dokuchaev, M y Exel, R. "Strong equivalence of graded algebras". [Preprint]. Publicado en: Mathematics (Rings and Algebras). 2024, arXiv.2201.03513, jul. 2024, pp.1-38. DOI: 10.48550/arXiv.2201.03513https://hdl.handle.net/20.500.12008/4837810.48550/arXiv.2201.03513Versión permitida preprint.Publicado también en: Journal of Algebra, 2024, 659(1): 818-858. DOI: 10.1016/j.jalgebra.2024.07.014We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. As to a more general idempotent graded algebra B, we point out that the Cohen-Montgomery duality holds for B, and B is graded-equivalent to a global skew group algebra. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that any product partial group action α is globalizable up to Morita equivalence; if such a globalization β is minimal, then the skew group algebras by α and β are graded-equivalent; moreover, β is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras are stably isomorphic as graded algebraSubmitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2025-02-13T14:48:11Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2201.03513v2.pdf: 428406 bytes, checksum: 91cf43ea50e63b8515652dc773ec032e (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2025-02-13T14:50:55Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2201.03513v2.pdf: 428406 bytes, checksum: 91cf43ea50e63b8515652dc773ec032e (MD5)Made available in DSpace by Camps Karina (karina.camps@seciu.edu.uy) on 2025-02-13T15:27:42Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2201.03513v2.pdf: 428406 bytes, checksum: 91cf43ea50e63b8515652dc773ec032e (MD5) Previous issue date: 202438 h.application/pdfenengarXivMathematics (Rings and Algebras). arXiv:2201.03513, jul. 2024, pp.1-38Las 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)MORITA EQUIVALENCERADED ALGEBRAPARTIAL ACTIONSKEW GROUP RINGSMASH PRODUCTStrong equivalence of graded algebrasPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAbadie, FernandoDokuchaev, MichaelExel, RuyLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/48378/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/48378/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Strong equivalence of graded algebras Abadie, Fernando MORITA EQUIVALENCE RADED ALGEBRA PARTIAL ACTION SKEW GROUP RING SMASH PRODUCT |
| status_str | submittedVersion |
| title | Strong equivalence of graded algebras |
| title_full | Strong equivalence of graded algebras |
| title_fullStr | Strong equivalence of graded algebras |
| title_full_unstemmed | Strong equivalence of graded algebras |
| title_short | Strong equivalence of graded algebras |
| title_sort | Strong equivalence of graded algebras |
| topic | MORITA EQUIVALENCE RADED ALGEBRA PARTIAL ACTION SKEW GROUP RING SMASH PRODUCT |
| url | https://hdl.handle.net/20.500.12008/48378 |
