Affine Kac-Moody symmetric spaces
Walter Freyn

TL;DR
This paper introduces and studies infinite dimensional affine Kac-Moody symmetric spaces, extending finite dimensional Riemannian symmetric space theory into a Lorentzian, infinite-dimensional setting with applications in mathematics and physics.
Contribution
It develops the theory of affine Kac-Moody symmetric spaces, classifies them similarly to finite dimensional cases, and explores their geometric and physical significance.
Findings
Classification into four types of Kac-Moody symmetric spaces.
They have Lorentzian structure and share properties with finite dimensional counterparts.
Applications in supergravity theories and M-theory.
Abstract
Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite dimensional generalization: Affine Kac-Moody symmetric spaces. Affine Kac-Moody symmetric spaces are infinite dimensional symmetric spaces associated to affine Kac-Moody groups. They have the structure of tame Fr\'echet manifolds; the natural Ad-invariant scalar product on affine Kac-Moody algebras is Lorentzian, making affine Kac-Moody symmetric spaces into Lorentzian symmetric spaces. Similar to affine Kac-Moody groups sharing most of their structure properties with simple Lie group, also Kac-Moody symmetric spaces share most of their structure properties with their finite dimensional Riemannian counterparts. In particular the classification of…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Algebra and Geometry
