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Koszul and Gorenstein properties for homogeneous algebras

Roland Berger·Nicolas Marconnet
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Abstract

Koszul property was generalized to homogeneous algebras of degree N>2 in [5], and related to N-complexes in [7]. We show that if the N-homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem [23] to A, i.e., there is a Poincare duality between Hochschild homology and cohomology of A, as for N=2.

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Roland Berger, Nicolas Marconnet. 2004-05-13. Koszul and Gorenstein properties for homogeneous algebras. https://arxiv.org/abs/math/0310070

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