For an affine algebraic variety X, we study the subgroup Autalg(X) of group regular automorphisms Aut(X) X generated by all connected subgroups. We prove that is nested, i.e., a direct limit subgroups Aut(X), if and only

We construct a model of the affine nil-Hecke algebra as a subalgebra of the Nichols-Woronowicz algebra associated to a Yetter-Drinfeld module over the affine Weyl group. We also discuss the Peterson isomorphism between the homology of the affine Grassmannian and the small quantum cohomology ring of the flag variety in terms of the braided differential calculus.

A closed subgroup H of the affine, algebraic group G is called observable if G/H is a quasi-affine algebraic variety. In this paper we define the notion of an observable subgroup of the affine, algebraic monoid M . We prove that a subgroup H of G is observable in M if and only if H is closed in M and there are “enough” H-semiinvariant functions in k[M ]. We show also that a closed, normal subgr...

In the following we will give an overview of our research area. Most of it belongs to the field of affine differential geometry. Geometry, as defined in Felix Klein’s Erlanger Programm, is the theory of invariants with respect to a given transformation group. In this sense affine geometry corresponds to the affine group (general linear transformations and translations) and it’s subgroups acting...