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HIGHER KOSZUL DUALITY FOR ASSOCIATIVE ALGEBRAS

Published online by Cambridge University Press:  01 October 2013

VLADIMIR DOTSENKO
Affiliation:
School of Mathematics, Trinity College Dublin, Dublin 2, Ireland e-mail: vdots@maths.tcd.ie
BRUNO VALLETTE
Affiliation:
Laboratoire J. A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France e-mail: brunov@unice.fr
Corresponding
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Abstract

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

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