Agustín García Iglesias

Finite-dimensional pointed Hopf algebras over \(\mathbb{S}_4\)

Let K be an algebraically closed field of characteristic 0. We conclude the classification of finite-dimensional pointed Hopf algebras whose group of group-likes is

An explicit description of the second cohomology group of a quandle

\mathbb{S}_4

Twisting Hopf algebras from cocycle deformations

. We also describe all pointed Hopf algebras over

Copointed Hopf algebras over S4

\mathbb{S}_5

Liftings of Nichols algebras of diagonal type III. Cartan type G2

whose infinitesimal braiding is associated to the rack of transpositions.

Lifting via cocycle deformation

We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several applications are given.

Liftings of Nichols algebras of diagonal type II. All liftings are cocycle deformations

Let H be a Hopf algebra. Any finite-dimensional lifting of

Finite-dimensional pointed or copointed Hopf algebras over affine racks☆

V\in {}^{H}_{H}\mathcal {YD}