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Poincaré–Birkhoff–Witt Theorem for Quadratic Algebras of Koszul Type

✍ Scribed by Alexander Braverman; Dennis Gaitsgory

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 185 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0122

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✦ Synopsis

In this paper we prove a general Poincare᎐Birkhoff᎐Witt theorem for quadratic Ḱoszul algebras. The result is similar to that obtained by Polischuk and Positselsky, but the proof is entirely different and uses algebraic deformation theory. In particular, we obtain a new proof of the classical PBW-theorem for Lie algebras, based on deformation theory.