Construction of quantized enveloping algebras by cocycle deformation

TL;DR

This paper introduces a new method using cocycle deformation to construct a class of Hopf algebras, including quantized enveloping algebras, simplifying the process compared to traditional quantum double constructions.

Contribution

It presents a novel cocycle deformation approach to build Hopf algebras from pre-Nichols algebras, extending known methods and avoiding complex relation checks.

Findings

Constructs Hopf algebras via cocycle deformation from pre-Nichols algebras

Generalizes quantum double constructions with simplified relations

Includes quantized enveloping algebras and their analogues

Abstract

By using cocycle deformation, we construct a certain class of Hopf algebras, containing the quantized enveloping algebras and their analogues, from what we call pre-Nichols algebras. Our construction generalizes in some sense the known construction by (generalized) quantum doubles, but unlike in the known situation, it saves us from difficulties in checking complicated defining relations.