On the Killing form of Lie Algebras in Symmetric Ribbon Categories

TL;DR

This paper explores the properties of the Killing form within Lie algebras in symmetric ribbon categories, advancing the understanding of their structure in a categorical framework.

Contribution

It establishes foundational results about the Killing form in symmetric ribbon categories, extending classical Lie algebra theory to a categorical context.

Findings

Killing form properties are characterized in symmetric ribbon categories.

Results connect categorical structures with classical Lie algebra invariants.

Provides groundwork for further structural analysis of Lie algebras in monoidal categories.

Abstract

As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.