Higher Koszul duality for associative algebras

Vladimir Dotsenko , Bruno Vallette (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We present a unifying framework for the key concepts and results of higher Koszul duality theory for N-homogeneous algebras: the Koszul complex, the candidate for the space of syzygies, and the higher operations on the Yoneda algebra. We give a universal description of the Koszul dual algebra under a new algebraic structure. For that we introduce a general notion: Gröbner bases for algebras over non-symmetric operads.

Domaines: Anneaux et algèbres [math.RA]; K-théorie et homologie [math.KT]

Vladimir Dotsenko, Bruno Vallette. Higher Koszul duality for associative algebras. Glasgow Mathematical Journal, 2013, 55 (A), pp.55-74. ⟨10.1017/S0017089513000505⟩. ⟨hal-00670319⟩