From Koszul duality to Poincaré duality

Details From Koszul duality to Poincaré duality From Koszul duality to Poincaré duality

2011-09-28

arxiv.org/abs/1109.6117v1

Mathematics

Quantum Algebra

Dedicated to Raymond Stora. 27 pages

Scientific paper

We discuss the notion of Poincar\'e duality for graded algebras and its
connections with the Koszul duality for quadratic Koszul algebras. The
relevance of the Poincar\'e 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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