Bosonization of curved Lie bialgebras

TL;DR

This paper explores the bosonization process for curved Lie bialgebras within Cartier's categorical framework, providing explicit examples and revealing connections to Nichols algebras over abelian groups.

Contribution

It demonstrates that bosonization can be consistently applied to curved Lie bialgebras using preadditive symmetric monoidal categories, and links these structures to Nichols algebras.

Findings

Bosonization is feasible for curved Lie bialgebras in this categorical setting.

Explicit examples illustrate the theory.

Deep relationship identified between curved Lie bialgebras and Nichols algebras over abelian groups.

Abstract

We use Cartier's preadditive symmetric monoidal categories to study Lie bialgebras. We prove that bosonization can be done consistently in this framework. In the last part of the paper we present explicit examples and indicate a deep relationship between certain curved Lie bialgebras and Nichols algebras over abelian groups.