Tame Fr\'echet submanifolds

We introduce the new class of submanifolds of co-Banach type in tame Fr\'echet manifolds and construct tame Fr\'echet submanifolds as inverse images of regular values of certain tame maps. Our method furnishes an easy way to construct tame Fr\'echet manifolds. The results presented are key ingredients in the construction of affine Kac-Moody symmetric spaces; they have also important applications in the study of isoparametric submanifolds in tame Fr\'echet spaces.Comment: arXiv admin note: text overlap with arXiv:1109.283

Kac-Moody symmetric spaces of Euclidean type

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.Comment: arXiv admin note: text overlap with arXiv:1109.283

Dimensions of Imaginary Root Spaces of Hyperbolic Kac--Moody Algebras

We discuss the known results and methods for determining root multiplicities for hyperbolic Kac--Moody algebras