Koszul equivalences in -algebras.

Lu, Di Ming; Palmieri, John H.; Wu, Quan Shui; Zhang, James J.

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$N$ -Koszul algebras, a summary.

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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.

Koszul duality for N-Koszul algebras

Roberto Martínez-Villa, Manuel Saorín (2005)

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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 $A_{\infty}$ 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.

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M. Doubek, Martin Markl, Petr Zima (2007)

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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....

Displaying similar documents to “Koszul equivalences in A ∞ -algebras.”

Displaying similar documents to “Koszul equivalences in $A_{\infty}$ -algebras.”