Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two
Tomasz Brzezi\'nski
TL;DR
This paper constructs differential calculi for certain algebraic structures and concludes that all affine pointed Hopf domains of Gelfand-Kirillov dimension two, excluding polynomial identity rings, are differentially smooth.
Contribution
It introduces new differential calculi for Ore extensions and classifies affine pointed Hopf domains of Gelfand-Kirillov dimension two as differentially smooth.
Findings
Constructed two-dimensional integrable differential calculi for specific Ore extensions.
Proved that all affine pointed Hopf domains of Gelfand-Kirillov dimension two (not PI rings) are differentially smooth.
Extended understanding of differential structures on algebraic domains.
Abstract
Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.
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