Kac-Moody symmetric spaces of Euclidean type

TL;DR

This paper explores Euclidean affine Kac-Moody symmetric spaces and their associated algebras, highlighting their unique status among Kac-Moody symmetric spaces not directly derived from classical affine Kac-Moody algebras.

Contribution

It provides a detailed investigation of Euclidean affine Kac-Moody symmetric spaces and introduces their orthogonal symmetric affine Kac-Moody algebras, emphasizing their distinct nature.

Findings

Identification of Euclidean affine Kac-Moody symmetric spaces

Characterization of their orthogonal symmetric affine Kac-Moody algebras

Highlighting their unique non-classical derivation

Abstract

We investigate in detail the class of Euclidean affine Kac-Moody symmetric spaces and their orthogonal symmetric affine Kac-Moody algebras (OSAKAs). These spaces are the only class of Kac-Moody symmetric spaces, that is not directly derived from affine Kac-Moody algebras in the classical sense.