Path group actions induced by sigma-actions and affine Kac-Moody symmetric spaces of group type

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.

Kac-Moody geometry

The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitely known representations as groups of operators. In this article we describe the infinite dimensional differential geometry associated to Kac-Moody groups: Kac-Moody symmetric spaces, isoparametric submanifolds in Hilbert space, polar actions on Hilbert spaces and universal geometric twin buildings.

Orthogonal affine Kac-Moody algebras

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 desc…

Kac-Moody李代数光滑补的不变量环

The Ring of Invariants for Smooth Completions of Kac-Moody Lie Algebras

证明了Kac-Moody李代数的标准光滑完备的不变量环是由中心系数和Killing型两个元素生成的.

Affine Kac-Moody symmetric spaces

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 Fréchet manifolds; the natural Ad-invariant scalar product on affine Kac-Moody algebras is Lorentzian, making affine Kac-Moody symmetric spaces into L…

Spin Structures of Kac-Moody Type

We study spin structures on affine Kac-Moody symmetric spaces and obtain sufficient conditions for their existence.\ As a by product of this, we obtain a spin-c representation of certain Kac-Moody quadratic subgroups of type E.