Quantum Field Theory and the Space of All Lie Algebras

2003/04/22 by William Gordon Ritter, Ritter, William Gordon
Mathematics · Physics and Astronomy · #17B81 #81T70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #math-ph #math.AG #math.GR #math.MP #msc:17B81 #msc:81T70

paper · pdf · doi:10.48550/arxiv.math-ph/0304031

12 pages, accepted for publication

openalex publication_date 2003/04/22 · arxiv created 2004/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The space M_n of all isomorphism classes of n-dimensional Lie algebras over a field k has a natural non-Hausdorff topology, induced from the Segal topology by the action of GL(n). One way of studying this complicated space is by topological invariants. In this article we propose a new class of invariants coming from quantum field theory, valid in any dimension, inspired by Jaffe's study of generalizations of the Witten index.

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