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arXiv · 1411.1982

Nonhomogeneous quadratic duality and curvature

Leonid Positselski
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Abstract

This is a slightly corrected version of the article published by Functional Analysis and its Applications in 1993. We define the quadratic duality for algebras with nonhomogeneous relations; the duality between the algebra of differential operators and the multiplicative de Rham complex is a classical example. The scalar part of the relations is interpreted as the curvature. Chern classes of nonhomogeneneous quadratic algebras are introduced as certain obstructions; the Chern-Simons classes are also discussed. The Poincare-Birkhoff-Witt theorem is considered in the context of the duality, and its simple proof is given.

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Leonid Positselski. 2014-11-10. Nonhomogeneous quadratic duality and curvature. https://doi.org/10.1007/bf01087537

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