Quantum Field Theory and the Space of All Lie Algebras
William Gordon Ritter
Abstract
The space Mn 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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