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arXiv · 1308.1998

Connected Hopf algebras and iterated Ore extensions

K. A. Brown·S. O'Hagan·J. J. Zhang·G. Zhuang
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Abstract

We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}] 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.

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K. A. Brown, S. O'Hagan, J. J. Zhang, G. Zhuang. 2013-08-08. Connected Hopf algebras and iterated Ore extensions. https://arxiv.org/abs/1308.1998

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