Abstract
In continuation of the articles (Liu J Algebra 299:841–853, 2006; Huang, J Algebra 321:2650–2669, 2009) we classify all finite-dimensional basic Hopf algebras of tame type over an algebraically closed field of characteristic 0 in this paper. As consequences, we show the following statements: (1) the representation dimension of a tame basic Hopf algebra is exactly 3, (2) for a basic Hopf algebra H, if \(\textrm{C}(H)\geq 3\) then it is wild. These conclusions verify a folklore conjecture and one of Rickard’s statements for the class of finite-dimensional basic Hopf algebras.
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