Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie
Supervisor(es): Solotar, Andrea - Lanzilotta, Marcelo
Resumen:
In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A).
| 2015 | |
|
Hochschild cohomology Toupie algebras Representaciones de álgebra Álgebras toupie. |
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| Español | |
| Universidad de la República | |
| COLIBRI | |
| http://hdl.handle.net/20.500.12008/9207 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0) |
| _version_ | 1807522818597847040 |
|---|---|
| author | Artenstein, Dalia |
| author_facet | Artenstein, Dalia |
| 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 Ciencias. Centro de Matemática |
| dc.creator.advisor.none.fl_str_mv | Solotar, Andrea Lanzilotta, Marcelo |
| dc.creator.none.fl_str_mv | Artenstein, Dalia |
| dc.date.accessioned.none.fl_str_mv | 2017-07-21T18:30:44Z |
| dc.date.available.none.fl_str_mv | 2017-07-21T18:30:44Z |
| dc.date.issued.none.fl_str_mv | 2015 |
| dc.description.abstract.none.fl_txt_mv | In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A). |
| dc.format.extent.es.fl_str_mv | 80 p. |
| dc.format.mimetype.none.fl_str_mv | aplication/pdf |
| dc.identifier.citation.es.fl_str_mv | ARTENSTEIN, Dalia. Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie [en línea] Tesis de doctorado. Universidad de la República (Uruguay). Facultad de Ciencias. PEDECIBA 2015. |
| dc.identifier.uri.none.fl_str_mv | http://hdl.handle.net/20.500.12008/9207 |
| dc.language.iso.none.fl_str_mv | es spa |
| dc.publisher.es.fl_str_mv | UR.FC |
| 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 | Hochschild cohomology Toupie algebras Representaciones de álgebra Álgebras toupie. |
| dc.title.none.fl_str_mv | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| dc.type.es.fl_str_mv | Tesis de doctorado |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/doctoralThesis |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/acceptedVersion |
| description | In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A). |
| eu_rights_str_mv | openAccess |
| format | doctoralThesis |
| id | COLIBRI_c56728c782c102c8ae3b7a33b133aa1b |
| identifier_str_mv | ARTENSTEIN, Dalia. Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie [en línea] Tesis de doctorado. Universidad de la República (Uruguay). Facultad de Ciencias. PEDECIBA 2015. |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | spa |
| language_invalid_str_mv | es |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/9207 |
| publishDate | 2015 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@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 Ciencias. Centro de Matemática2017-07-21T18:30:44Z2017-07-21T18:30:44Z2015ARTENSTEIN, Dalia. Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie [en línea] Tesis de doctorado. Universidad de la República (Uruguay). Facultad de Ciencias. PEDECIBA 2015.http://hdl.handle.net/20.500.12008/9207In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A).Submitted by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2017-07-21T18:30:44Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) ARTENSTEIN.pdf: 415426 bytes, checksum: 97cd31a47f6d04d37cd5eae1bf26adac (MD5)Made available in DSpace on 2017-07-21T18:30:44Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) ARTENSTEIN.pdf: 415426 bytes, checksum: 97cd31a47f6d04d37cd5eae1bf26adac (MD5) Previous issue date: 201580 p.aplication/pdfesspaUR.FCLas 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)Hochschild cohomologyToupie algebrasRepresentaciones de álgebraÁlgebras toupie.Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupieTesis de doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaArtenstein, DaliaSolotar, AndreaLanzilotta, MarceloUniversidad de la República (Uruguay). Facultad de Ciencias. PEDECIBADoctor en MatemáticaLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/9207/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://localhost:8080/xmlui/bitstream/20.500.12008/9207/2/license_url4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-80http://localhost:8080/xmlui/bitstream/20.500.12008/9207/3/license_textd41d8cd98f00b204e9800998ecf8427eMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-80http://localhost:8080/xmlui/bitstream/20.500.12008/9207/4/license_rdfd41d8cd98f00b204e9800998ecf8427eMD54ORIGINALARTENSTEIN.pdfARTENSTEIN.pdfapplication/pdf415426http://localhost:8080/xmlui/bitstream/20.500.12008/9207/1/ARTENSTEIN.pdf97cd31a47f6d04d37cd5eae1bf26adacMD5120.500.12008/92072021-03-03 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Universidadhttps://udelar.edu.uy/https://www.colibri.udelar.edu.uy/oai/requestmabel.seroubian@seciu.edu.uyUruguayopendoar:47712024-07-25T14:29:56.246722COLIBRI - Universidad de la Repúblicafalse |
| spellingShingle | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie Artenstein, Dalia Hochschild cohomology Toupie algebras Representaciones de álgebra Álgebras toupie. |
| status_str | acceptedVersion |
| title | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| title_full | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| title_fullStr | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| title_full_unstemmed | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| title_short | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| title_sort | Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie |
| topic | Hochschild cohomology Toupie algebras Representaciones de álgebra Álgebras toupie. |
| url | http://hdl.handle.net/20.500.12008/9207 |
