Extending lazy 2-cocycles on Hopf algebras and lifting projective representations afforded by them

TL;DR

This paper investigates the extension and lifting properties of lazy 2-cocycles in Hopf algebras, focusing on their applications to Drinfeld doubles, Radford biproducts, and projective representations.

Contribution

It introduces new methods for extending lazy 2-cocycles to complex algebraic structures and explores their role in lifting projective representations.

Findings

Lazy 2-cocycles can be extended to Drinfeld doubles and Radford biproducts.

Yetter-Drinfeld data can be derived from lazy 2-cocycles.

Lifting of projective representations is achieved using lazy 2-cocycles.

Abstract

We study some problems related to lazy 2-cocycles, such as: extension of (lazy) 2-cocycles to a Drinfeld double and to a Radford biproduct, Yetter-Drinfeld data obtained from lazy 2-cocycles, lifting of projective representations afforded by lazy 2-cocycles.