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From Koszul duality to Poincaré duality

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Abstract

We discuss the notion of Poincaré duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincaré duality is pointed out for the existence of twisted potentials associated to Koszul algebras as well as for the extraction of a good generalization of Lie algebras among the quadratic-linear algebras.

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  1. Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris Sud 11, Bâtiment 210, F-91 405, Orsay Cedex, France

    MICHEL DUBOIS-VIOLETTE

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  1. MICHEL DUBOIS-VIOLETTE
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Correspondence to MICHEL DUBOIS-VIOLETTE.

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DUBOIS-VIOLETTE, M. From Koszul duality to Poincaré duality. Pramana - J Phys 78, 947–961 (2012). https://doi.org/10.1007/s12043-012-0320-7

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