Koszul duality of translation- and Zuckerman functors.
Ryom-Hansen, Steen (2004)
Journal of Lie Theory
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Ryom-Hansen, Steen (2004)
Journal of Lie Theory
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Keller, Bernhard (2001)
Homology, Homotopy and Applications
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Martínez-Villa, Roberto, Zacharia, Dan (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Green, E.L., Marcos, E.N., Martínez-Villa, R., Zhang, Pu (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Dag Madsen (2006)
Colloquium Mathematicae
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Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.
Roberto Martínez-Villa, Manuel Saorín (2005)
Colloquium Mathematicae
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The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.
Tadeusz Józefiak (1976)
Fundamenta Mathematicae
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Tadeusz Józefiak (1972)
Fundamenta Mathematicae
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Ionuţ Ciocan-Fontanine, Mikhail Kapranov (2001)
Annales scientifiques de l'École Normale Supérieure
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M. Doubek, Martin Markl, Petr Zima (2007)
Archivum Mathematicum
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First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation....
R. M. Aquino, E. L. Green, E. N. Marcos (2002)
Colloquium Mathematicae
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Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...