Additive Deformations of Braided Hopf Algebras

TL;DR

This paper extends the concept of additive deformations from bialgebras to braided bialgebras, including *-structures, and establishes a general Schoenberg correspondence with illustrative examples.

Contribution

It generalizes additive deformation theory to braided Hopf algebras and proves a broad Schoenberg correspondence applicable in this setting.

Findings

Additive deformations are extended to braided bialgebras.

A general Schoenberg correspondence is established for these structures.

Several examples demonstrate the theoretical results.

Abstract

Additive deformations of bialgebras in the sense of J. Wirth, i.e. deformations of the multiplication map fulfilling a certain compatibility condition w.r.t. the coalgebra structure, can be generalized to braided bialgebras. The theorems for additive deformations of Hopf algebras can also be carried over to that case. We consider *-structures and prove a general Schoenberg correspondence in this context. Finally we give some examples.