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dc.contributor.author
Cibils, Claude
dc.contributor.author
Lanzilotta, Marcelo
dc.contributor.author
Marcos, Eduardo N.
dc.contributor.author
Solotar, Andrea Leonor
dc.date.available
2021-07-19T18:47:09Z
dc.date.issued
2019-10
dc.identifier.citation
Cibils, Claude; Lanzilotta, Marcelo; Marcos, Eduardo N.; Solotar, Andrea Leonor; Hochschild cohomology of algebras arising from categories and from bounded quivers; European Mathematical Society; Journal of Noncommutative Geometry; 13; 3; 10-2019; 1011-1053
dc.identifier.issn
1661-6952
dc.identifier.uri
http://hdl.handle.net/11336/136429
dc.description.abstract
The main objective of this paper is to provide a theory for computing the Hochschild cohomology of algebras arising from a linear category with finitely many objects and zero compositions. For this purpose, we consider such a category using an ad hoc quiver Q, with an algebra associated to each vertex and a bimodule to each arrow. The computation relies on cohomological functors that we introduce, and on the combinatorics of the quiver. One point extensions are occurrences of this situation, and Happel’s long exact sequence is a particular case of the long exact sequence of cohomology that we obtain via the study of trajectories of the quiver. We introduce cohomology along paths, and we compute it under suitable Tor vanishing hypotheses. The cup product on Hochschild cohomology enables us to describe the connecting homomorphism of the long exact sequence. Algebras arising from a linear category where the quiver is the round trip one, provide square matrix algebras which have two algebras on the diagonal and two bimodules on the corners. If the bimodules are projective, we show that five-terms exact sequences arise. If the bimodules are free of rank one, we provide a complete computation of the Hochschild cohomology. On the other hand, if the corner bimodules are projective without producing new cycles, Hochschild cohomology in large enough degrees is that of the product of the algebras on the diagonal. As a by-product, we obtain some families of bound quiver algebras which are of infinite global dimension, and have Hochschild cohomology zero in large enough degrees.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
European Mathematical Society
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
COHOMOLOGY
dc.subject
FIVE-TERM EXACT SEQUENCE
dc.subject
HOCHSCHILD
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QUIVER
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SQUARE ALGEBRAS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Hochschild cohomology of algebras arising from categories and from bounded quivers
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-27T18:10:01Z
dc.journal.volume
13
dc.journal.number
3
dc.journal.pagination
1011-1053
dc.journal.pais
Suiza
dc.journal.ciudad
Zürich
dc.description.fil
Fil: Cibils, Claude. Université Montpellier II; Francia
dc.description.fil
Fil: Lanzilotta, Marcelo. Universidad de la Republica; Uruguay
dc.description.fil
Fil: Marcos, Eduardo N.. Universidade de Sao Paulo; Brasil
dc.description.fil
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Journal of Noncommutative Geometry
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.4171/JNCG/344
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=13&iss=3&rank=6
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