De-equivariantization of Hopf algebras

TL;DR

This paper explores the process of de-equivariantizing Hopf algebras using Tannakian methods, leading to the construction of new coquasi-Hopf algebras from graded pointed Hopf algebras.

Contribution

It introduces a novel approach to de-equivariantization of Hopf algebras and constructs a new family of coquasi-Hopf algebras based on this technique.

Findings

Realization of de-equivariantization as comodules over coquasi-bialgebras

Construction of a family of coquasi-Hopf algebras $A(H,G,\

,

Abstract

We study the de-equivariantization of a Hopf algebra by an affine group scheme and we apply Tannakian techniques in order to realize it as the tensor category of comodules over a coquasi-bialgebra. As an application we construct a family of coquasi-Hopf algebras $A(H,G,\Phi)$ attached to a coradically-graded pointed Hopf algebra $H$ and some extra data.