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- W2019959507 abstract "Let $k$ be an algebraically closed field. In 2007, D.-M. Lu, Q.-S. Wu, and J. J. Zhang asked the following question: Besides the group algebras $kmathbb {Z},;kmathbb {D}$ and infinite dimensional prime Taft algebras, are there other noetherian affine prime regular Hopf algebras of GK-dimension 1? In this paper, we give a new one. Another problem posed by Lu, Wu, and Zhang can also be resolved by this example. Assuming $H$ is a noetherian affine prime regular Hopf algebra of GK-dimension 1, we show that gr$H:= bigoplus _{sgeq 0}J_{iq}^{s}/J_{iq}^{s+1}$, as a Hopf algebra, is isomorphic to an infinite dimensional prime Taft algebra. This gives a characterization of infinite dimensional prime Taft algebras." @default.
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- W2019959507 date "2008-10-29" @default.
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- W2019959507 title "On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1" @default.
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- W2019959507 doi "https://doi.org/10.1090/s0002-9939-08-09034-5" @default.
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