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| Main Authors: | , |
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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17710668 |
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Table of Contents:
- This paper explores the intricate relationship between Lie algebra deformations and categorical structures, proposing novel frameworks for their categorical realization. Lie algebras, fundamental algebraic objects in mathematics and physics, often undergo deformations which alter their algebraic structure while preserving certain essential properties. Understanding these deformations is crucial for various applications, from quantum field theory to geometric mechanics. Traditional deformation theory, pioneered by Gerstenhaber and Nijenhuis-Richardson, primarily employs homological methods to classify and characterize deformations. This work extends this perspective by investigating how the process of deformation, its infinitesimal components, and the obstructions to integration can be naturally interpreted and structured within suitable categories. We delve into the utility of higher category theory, particularly 2-categories and (infinity,1)-categories, as well as operadic structures, to provide a richer, more abstract understanding of deformation phenomena. By establishing functorial relationships and identifying deformation moduli spaces with objects or morphisms in specific categories, this paper aims to unify classical deformation theory with advanced categorical insights, offering new computational tools and conceptual clarity. We demonstrate that categorical realizations provide not only a systematic classification but also deeper insights into the geometric and topological underpinnings of Lie algebra deformations.