Basic Hopf algebras of tame type.
The classification of all finite-dimensional basic Hopf algebras of tame type over an algebraically closed field of characteristic 0 is given. This is a continuation of the articles [\textit{G. Liu}, J. Algebra 299, No. 2, 841-853 (2006; Zbl 1110.16045); \textit{H.-L. Huang} and \textit{G. Liu}, J. Algebra 321, No. 9, 2650-2669 (2009; Zbl 1173.16018)], where classification of all radically graded basic Hopf algebras of tame type and classification of basic Hopf algebras of finite representation type were given, respectively. As a consequence it is proved that the representation dimension of a tame basic Hopf algebra is exactly \(3\). Moreover, the author shows that for a basic Hopf algebra \(H\), if \(C(H)\geq 3\) then it is wild, where \(C(H)\) is the complexity of \(H\). The last corollary is connected with Rickard's conjecture and statement about complexity of modules over self-injective tame algebras.
scientific article; zbMATH DE number 6175492
scientific article