Geodesic
UNIVERSAL ENVELOPING ALGEBRAS OF PBW TYPE*
Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 9-26

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DOI

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.
DOI : 10.1017/S0017089511000310
Mots-clés : Primary 16W30, Secondary 16S30 
ARDIZZONI, ALESSANDRO. UNIVERSAL ENVELOPING ALGEBRAS OF PBW TYPE*. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 9-26. doi: 10.1017/S0017089511000310
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