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 Universal Enveloping Algebras of PBW Type

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We continue our investigation of the general notion of universal enveloping algebra introduced in A. Ardizzoni, \emph{A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras}, J. Algebra \textbf{327} 2011, no. 1, 337-365. Namely we study when such an algebra is of PBW type, meaning that a suitable PBW type theorem holds. We discuss the problem of finding a basis for a universal enveloping algebra of PBW type: As an application we recover the PBW basis both of an ordinary universal enveloping algebra and of a restricted enveloping algebra. We prove that a universal enveloping algebra is of PBW type if and only if it is cosymmetric. We characterize braided bialgebra liftings of Nichols algebras as universal enveloping algebras of PBW type.

Author: Alessandro Ardizzoni

Source: https://archive.org/

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