2013/08/08 by Brown, K. A., O'Hagan, S., Zhang, J. J. +1 · 2 citations
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1308.1998
We investigate when a skew polynomial extension T = R[x; σ, δ] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated.