We continue our investigation of the general notion of universal enveloping algebra introduced in [A. Ardizzoni, "A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras", J. Algebra 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.
Universal Enveloping Algebras of PBW Type
ARDIZZONI, Alessandro
2012-01-01
Abstract
We continue our investigation of the general notion of universal enveloping algebra introduced in [A. Ardizzoni, "A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras", J. Algebra 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.File | Dimensione | Formato | |
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