Orthogonal affine Kac-Moody algebras

TL;DR

This paper introduces and classifies OSAKAs, algebraic structures that connect affine Kac-Moody symmetric spaces with affine Kac-Moody algebras, advancing the understanding of infinite-dimensional symmetric spaces.

Contribution

It defines OSAKAs and provides a classification, establishing a foundational algebraic framework for affine Kac-Moody symmetric spaces.

Findings

Introduction of OSAKAs as algebraic structures

Classification of OSAKAs

Linking affine Kac-Moody symmetric spaces with algebras

Abstract

Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues known as Kac-Moody groups. We solve this problem and construct affine Kac-Moody symmetric spaces in a series of several papers. This paper focuses on the algebraic side: More precisely, we introduce OSAKAs, the algebraic structures used to describe the connection between affine Kac-Moody symmetric spaces and affine Kac-Moody algebras and describe their classification.