Minimal Triangular Structures on Abelian Extensions

We study minimal triangular structures on abelian extensions. In particular, we construct a family of minimal triangular semisimple Hopf algebras and prove that the Hopf algebra \(H_{b:y}\) $H_{b:y}$ in the semisimple Hopf algebras of dimension 16 classified by Y. Kashina in 2000 is minimal triangular Hopf algebra with smallest dimension among non-trivial semisimple triangular Hopf algebras (i.e. not group algebras or their dual).