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UNIVERSAL ENVELOPING ALGEBRAS OF PBW TYPE*

Published online by Cambridge University Press:  02 August 2011

ALESSANDRO ARDIZZONI
ALESSANDRO ARDIZZONI*
Affiliation:
University of Ferrara, Department of Mathematics, Via Machiavelli 35, Ferrara I-44121, Italy e-mail: alessandro.ardizzoni@unife.it
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Abstract

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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(1) (2011), 337–365]. Namely, we study a universal enveloping algebra when it is of Poincaré–Birkhoff–Witt (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 characterise braided bialgebra liftings of Nichols algebras as universal enveloping algebras of PBW type.

Keywords

Primary 16W30Secondary 16S30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 9 - 26
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

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