Braided Hopf Algebras and Differential Calculus

TL;DR

This paper explores the structure of differential calculus on quantum groups, revealing it as a projection of a cross product involving braided Hopf algebras and quantum doubles, leading to a super-Hopf algebra framework.

Contribution

It introduces a novel perspective by representing the algebra of bicovariant differential calculus as a projection of a cross product with braided Hopf algebras and quantum doubles.

Findings

Differential calculus algebra is a projection of a cross product.

Super-Hopf algebra can be reconstructed via exterior derivative extension.

Provides a new algebraic framework for quantum group calculus.

Abstract

We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.