Skip to main content Accessibility help




The goal of this article is to study the coaugmented curved A-coalgebra structure of the Koszul codual of a filtered dg algebra over a field k. More precisely, we first extend one result of B. Keller that allowed to compute the A-coalgebra structure of the Koszul codual of a nonnegatively graded connected algebra to the case of any unitary dg algebra provided with a nonnegative increasing filtration whose zeroth term is k. We then show how to compute the coaugmented curved A-coalgebra structure of the Koszul codual of a Poincaré-Birkhoff-Witt (PBW) deformation of an N-Koszul algebra.



Hide All
1. Berger, R., Koszulity for nonquadratic algebras, J. Algebra 239 (2) (2001), 705734.
2. Berger, R. and Ginzburg, V., Higher symplectic reflection algebras and non-homogeneous N-Koszul property, J. Algebra 304 (1) (2006), 577601.
3. Fløystad, G. and Vatne, J. E., PBW-deformations of N-Koszul algebras, J. Algebra 302 (1) (2006), 116155.
4. Herscovich, E., On the multi-Koszul property for connected algebras, Doc. Math. 18 (2013), 13011347.
5. Herscovich, E., Using torsion theory to compute the algebraic structure of Hochschild (co)homology, Homology Homotopy Appl. 20 (1) (2018), 117–139.
6. Herscovich, E., Solotar, A. and Suárez-Álvarez, M., PBW-deformations and deformation à la Gerstenhaber of N-Koszul algebras, J. Noncommut. Geom. 8 (2) (2014), 505539.
7. Hinich, V., Homological algebra of homotopy algebras, Commun. Algebra 25 (10) (1997), 32913323.
8. Keller, B., The A-infinity structure of the Yoneda algebra of a generalized Koszul algebra, International Conference on Representations of Algebras (ICRA X), Toronto (2002).
9. Positselski, L., Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, Mem. Amer. Math. Soc. 212 (996) (2011), vi+133.
10. Prouté, A., A -structures. Modèles minimaux de Baues-Lemaire et Kadeishvili et homologie des fibrations, Repr. Theory Appl. Categ. 21 (2011), 199 (French). Reprint of the 1986 original; with a preface to the reprint by Jean-Louis Loday.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed