On Braided Quantum Groups

TL;DR

This paper introduces a braided generalization of quantum groups, addressing geometric limitations and deriving braid-type equations from foundational axioms, thus expanding the algebraic framework of quantum groups.

Contribution

It presents a novel braided framework for quantum groups that overcomes geometric inhomogeneity and derives key relations from axioms.

Findings

Braided quantum groups generalize standard quantum groups.

Braid-type equations follow from initial axioms.

Foundations for braided algebraic relations are established.

Abstract

A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All braid-type equations appear as a consequence of initial axioms. Braided counterparts of basic algebraic relations between fundamental entities of the standard theory are found.