The University of Montana
Department of Mathematical Sciences

Technical report #7/2006

Grassmannians Of Two-Sided Vector Spaces

Adam Nyman
Department of Mathematical Sciences
University of Montana

Abstract

Let be an extension of fields, and let be a k-algebra. We study parameter spaces of m-dimensional subspaces of which are invariant under A. The space , whose R-rational points are A-invariant, free rank m summands of , is well known. We construct a distinct parameter space, , which is a fiber product of a Grassmannian and the projectivization of a vector space. We then study the intersection , which we denote by . Under suitable hypotheses on A, we construct affine open subschemes of and which cover their K-rational points. We conclude by using , , and to construct parameter spaces of two-sided subspaces of two-sided vector spaces.

Keywords: Grassmannian, two-sided vector space, noncommutative vector bundle, bimodule.

AMS Subject Classification: Primary 15A03, 14M15, 16D20; Secondary 14A22.

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