Lie algebras in symmetric monoidal categories
Quantum Algebra
2015-03-20 v3 Algebraic Geometry
Rings and Algebras
Representation Theory
Abstract
We study algebras defined by identities in symmetric monoidal categories. Our focus is on Lie algebras. Besides usual Lie algebras, there are examples appearing in the study of knot invariants and Rozansky-Witten invariants. Our main result is a proof of Westbury's conjecture for K3-surface: there exists a Lie algebra homomorphism from Vogel's universal simple Lie algebra to the Lie algebra describing the Rozansky-Witten invariants of a K3-surface. Most of the paper involves setting up a proper language to discuss the problem and we formulate nine open questions as we proceed.
Keywords
Cite
@article{arxiv.1205.3705,
title = {Lie algebras in symmetric monoidal categories},
author = {Dmitriy Rumynin},
journal= {arXiv preprint arXiv:1205.3705},
year = {2015}
}
Comments
Minor corrections all around. Now it has an answer to Question 7, due to J. Sawon