Open quotients of trivial vector bundles

Locally trivial quantum vector bundles and associated vector bundles

We define locally trivial quantum vector bundles (QVB) and construct such QVB associated to locally trivial quantum principal fibre bundles. The construction is quite analogous to the classical construction of associated bundles. A covering of such bundles is induced from the covering of the subalgebra of coinvariant elements of the principal bundle. There exists a differential structure on the...

Stably Trivial Equivariant Algebraic Vector Bundles

Let G be a reductive algebraic group over e, let F be a G-module, and let B be an affine G-variety, i.e., an affine variety with an algebraic action of G. Then B x F is in a natural way a G-vector bundle over B, which we denote by F. (All vector bundles here are algebraic.) A G-vector bundle over B is called trivial if it is isomorphic to F for some G-module F . From the endomorphism ring R of ...

Essentially Finite Vector Bundles on Varieties with Trivial Tangent Bundle

Let X be a smooth projective variety, defined over an algebraically closed field of positive characteristic, such that the tangent bundle TX is trivial. Let FX : X −→ X be the absolute Frobenius morphism of X. We prove that for any n ≥ 1, the n–fold composition Fn X is a torsor over X for a finite group–scheme that depends on n. For any vector bundle E −→ X, we show that the direct image (Fn X)...

Locally trivial W∗-bundles

Knizhnik-zamolodchikov Bundles Are Topologically Trivial

We prove that the vector bundles at the core of the KnizhnikZamolodchikov and quantum constructions of braid groups representations are topologically trivial bundles. We provide partial generalizations of this result to generalized braid groups. A crucial intermediate result is that the representation ring of the symmetric group on n letters is generated by the alternating powers of its natural...