Lifting via cocycle deformation

GARCÍA IGLESIAS, AGUSTÍN

Quito

Congreso; Coloquio Latinoamericano de Álgebra; 2017

Pontificia Universidad Católica del Ecuador

Let V be a Yetter-Drinfeld module over a cosemisimple Hopf algebra H such that the Nichols algebra B(V) is finite-dimensional.We present a strategy, based on cocycle deformations, to compute all liftings of V; that is all Hopf algebras L with gr(L) = B(V) #H , where gr(L) stands for the graded Hopf algebra associated to the coradical filtration of L.When V is of diagonal type, we show that this method is exhaustive and reduces the problem to a (hard) algorithmic computation.  After the works of Heckenberger and Angiono, this corresponds to the final step in the Lifting Program developed by Andruskiewitsch and Schneider to classify all finite-dimensional pointed Hopf algebras with abelian group of group-like elements.When V is of rack type, this strategy produces new examples of pointed and copointed Hopf algebras: we shall also present the classification of finite-dimensional copointed Hopf algebras over the symmetric group s4