Complex-analytic quotients of algebraic $$G$$ G -varieties

Quantized Primitive Ideal Spaces as Quotients of Affine Algebraic Varieties

Given an affine algebraic variety V and a quantization Oq(V ) of its coordinate ring, it is conjectured that the primitive ideal space of Oq(V ) can be expressed as a topological quotient of V . Evidence in favor of this conjecture is discussed, and positive solutions for several types of varieties (obtained in joint work with E. S. Letzter) are described. In particular, explicit topological qu...

Controlled Algebraic G-theory

This paper extends the notion of geometric control in algebraic K-theory from additive categories with split exact sequences to other exact structures. In particular, we construct exact categories of modules over a noetherian ring filtered by subsets of a metric space and sensitive to the large scale properties of the space. The algebraic K-theory of these categories is related to the controlle...

Neighborhoods of Analytic Varieties in Complex Manifolds

Computation of Weight Lattices of G-varieties

Let G be a connected reductive group. To any irreducible G-variety X one assigns the lattice generated by all weights of B-semiinvariant rational functions on X , where B is a Borel subgroup of G. This lattice is called the weight lattice of X . We establish algorithms for computing weight lattices for homogeneous spaces and affine homogeneous vector bundles. For affine homogeneous spaces of ra...

Computation of Weyl Groups of G-varieties

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of G-varieties (affine...