We construct certain integral structures for the cores of reduced tame extended affine Lie algebras rank at least 2. One main tools to achieve this is a generalization Chevalley automorphisms in context algebras. As an application, groups type associated adjoint representation are defined over arbitrary fields.

The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners of double affine Hecke algebras.

Let G = SpecA be an affine functor of monoids. We prove that A∗ is the enveloping functor of algebras of G and that the category of Gmodules is equivalent to the category of A∗-modules. Moreover, we prove that the category of affine functors of monoids is anti-equivalent to the category of functors of affine bialgebras. Applications of these results include Cartier duality, neutral Tannakian du...

In finite-dimensional simple Lie algebras and affine Kac-Moody algebras, Chevalley involutions are crucial ingredients of the modular theory. Towards establishing theory for extended we investigate existence “Chevalley involutions” tori algebras. We first discuss how to lift a involution from centerless core which is characterized be torus then entire algebra. prove by type-dependent argument t...