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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. This notion also extends and generalizes the one recently introduced by the author and A. Rey, which was for the particular case of algebras further assumed to be finitely generated in degree 1 and with a finite dimensional space of relations. The idea of this new notion for this generality, which should be perhaps considered as a probably interesting common property for several of these algebras, was to find a grading independent description of some of the more appealing features shared by all generalized Koszul algebras. It 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 in any natural manner. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, similar to the existing one for homogeneous algebras, 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 a very explicit description of the A∞-algebra structure of the Yoneda algebra of a multi-Koszul algebra, which has a similar pattern as for the case of generalized Koszul algebras. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K2 algebra in the sense of T. Cassidy and B. Shelton.

Registro:

Documento: Artículo
Título:On the Multi-Koszul property for connected algebras
Autor:Herscovich, E.
Filiación:Institut Joseph Fourier, Université Grenoble I, France
Departamento deMatemática, FCEyN, Universidad de Buenos Aires, Argentina
Palabras clave:A∞-algebras; Homological algebra; Koszul algebra; Yoneda algebra
Año:2013
Volumen:18
Número:2013
Página de inicio:1301
Página de fin:1347
Título revista:Documenta Mathematica
Título revista abreviado:Doc. Math.
ISSN:14310635
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v18_n2013_p1301_Herscovich

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Citas:

---------- APA ----------
(2013) . On the Multi-Koszul property for connected algebras. Documenta Mathematica, 18(2013), 1301-1347.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v18_n2013_p1301_Herscovich [ ]
---------- CHICAGO ----------
Herscovich, E. "On the Multi-Koszul property for connected algebras" . Documenta Mathematica 18, no. 2013 (2013) : 1301-1347.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v18_n2013_p1301_Herscovich [ ]
---------- MLA ----------
Herscovich, E. "On the Multi-Koszul property for connected algebras" . Documenta Mathematica, vol. 18, no. 2013, 2013, pp. 1301-1347.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v18_n2013_p1301_Herscovich [ ]
---------- VANCOUVER ----------
Herscovich, E. On the Multi-Koszul property for connected algebras. Doc. Math. 2013;18(2013):1301-1347.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v18_n2013_p1301_Herscovich [ ]