Construction of quantized enveloping algebras by cocycle deformation

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.

To appear in a theme issue of the Arabian Journal for Science and Engineering. The published version will renumber the sections so that for example, Theorem 3.10 in this version will be called Theorem 4.10

References in corpus (1)

• Pointed and copointed Hopf algebras as cocycle deformations

Cited by in corpus (12)

• A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras
• Flatness and freeness properties of the generic Hopf Galois extensions
• Multiparameter quantum groups at roots of unity
• Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras
• Twisted deformations vs. cocycle deformations for quantum groups
• A First Sight Towards Primitively Generated Connected Braided Bialgebras
• Multiparameter quantum groups, bosonizations and cocycle deformations
• Schrödinger representations from the viewpoint of monoidal categories
• Handlebody-knot invariants derived from unimodular Hopf algebras
• Hopf ideals of the generalized quantum double associated to skew-paired Nichols algebras
• Simple modules over finite quantum groups and their Drinfel'd doubles
• Generalized $q$-boson algebras and their integrable modules