Lifting of Nichols Algebras of Type A 2 and Pointed Hopf Algebras of Order p 4

We compute all finite-dimensional Hopf algebras whose coradical is the group algebra of an abelian group Γ and such that gr(A) ≅ ℬ(V)#k[Γ], V a 2-dimensional Yetter-Drinfeld module over Γ of type A ₂. We classify pointed Hopf algebras of order p ⁴ up to isomorphism and show that the number of quasi-isomorphism types is finite.