On locally trivial deformations

Locally trivial W∗-bundles

Gauge transformations on locally trivial quantum principal fibre bundles

We consider in this paper gauge transformations on locally trivial quantum principal fibre bundles (QPFB). If P , B, H , are the algebras of the total space, the base space, the structure group of the bundle, left (right) gauge transformations are defined as automorphisms of the left (right) B-module P which are adapted to the coaction of the Hopf algebra H and to the covering related to the lo...

Connections on locally trivial quantum principal fibre bundles

Budzyński and Kondracki ([3]) have introduced a notion of locally trivial quantum principal fibre bundle making use of an algebraic notion of covering, which allows a reconstruction of the bundle from local pieces. Following this approach, we construct covariant differential algebras and connections on locally trivial quantum principal fibre bundles by gluing together such locally given geometr...

Tameness of some locally trivial pseudovarieties

Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.

Rationally trivial quadratic spaces are locally trivial:III

It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R such that q(v) = 0. If char(R) = 2, then in the case of even n we assume that q is a non-singular space in the sense of [Kn] and...