Existence of Hopf subalgebras of GK-dimension two. (English) Zbl 1235.16031
Let \(H\) be a pointed Hopf algebra over an algebraically closed field \(K\) of characteristic zero. It is shown that if \(H\) is a domain with finite Gelfand-Kirillov dimension greater than or equal to \(2\) then \(H\) contains a Hopf subalgebra of Gelfand-Kirillov dimension \(2\). More precisely, a list of such possible Hopf subalgebras is provided, which includes the group algebra of the free Abelian group of rank \(2\), the enveloping algebra of a \(2\)-dimensional Lie algebra, and two classes of algebras introduced by K. R. Goodearl and J. J. Zhang [in J. Algebra 324, No. 11, 3131-3168 (2010; Zbl 1228.16030)].
Reviewer: Jan Okniński (Warszawa)
Keywords:
pointed Hopf algebras; Gelfand-Kirillov dimension; GK-dimension; integral domains; universal enveloping algebrasCitations:
Zbl 1228.16030References:
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