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dc.contributor.author
Herscovich Ramoneda, Estanislao Benito
dc.date.available
2017-04-06T20:45:59Z
dc.date.issued
2013-12
dc.identifier.citation
Herscovich Ramoneda, Estanislao Benito; On the multi-Koszul property for connected algebras; Univ Bielefeld; Documenta Mathematica; 18; 12-2013; 1301-1347
dc.identifier.uri
http://hdl.handle.net/11336/14932
dc.description.abstract
In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras, which were in turn an extension of Koszul algebras introduced by S. Priddy. It also extends and generalizes the definition recently introduced by the author and A. Rey. In order to simplify the exposition we consider the minimal graded projective resolution of the algebra A as a bimodule, which may be used to compute the corresponding Hochschild (co)homology groups. This new definition includes several new interesting examples, e.g. the super Yang-Mills algebras introduced by M. Movshev and A. Schwarz, which are not generalized Koszul or even multi-Koszul for the previous definition given by the author and Rey. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, and we show that several of the typical homological computations performed for the generalized Koszul algebras are also possible in this more general setting. In particular, we give an explicit description of the A_infinity-algebra structure of the Yoneda algebra of a multi-Koszul algebra. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K_2 algebra in the sense of T. Cassidy and B. Shelton.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Univ Bielefeld
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Koszul Algebra
dc.subject
Yoneda Algebra
dc.subject
Homological Algebra
dc.subject
A_Infinity Algebras
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On the multi-Koszul property for connected algebras
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-04-05T15:11:43Z
dc.identifier.eissn
1431-0643
dc.journal.volume
18
dc.journal.pagination
1301-1347
dc.journal.pais
Alemania
dc.description.fil
Fil: Herscovich Ramoneda, Estanislao Benito. Université Grenoble I; Francia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Documenta Mathematica
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.math.uni-bielefeld.de/documenta/vol-18/41.pdf
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