Quadratic differential algebras generated by Euclidean spaces. Michel Dubois-Violette & Giovanni Landi
23/01/2020
Abstract:
We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a differential calculus over the quadratic algebra of its elements of differential degree zero. This generalizes for arbitrary quadratic algebras the differential graded algebra of exterior polynomial differential forms for the algebra of polynomial functions on ℝn. We investigate the structure of these differential algebras and their connection with the Koszul complexes of quadratic algebras.
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