2010/08/26 by Alessandro Ardizzoni, Ardizzoni, Alessandro
Mathematics · #16S30 #16W30 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16S30 #msc:16W30
paper · pdf · doi:10.48550/arxiv.1008.4523
arxiv created 2010/12/23 · arxiv updated 2010/12/24
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.