Locally trivial W∗-bundles

Locally trivial W∗-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...

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...

The $w$-FF property in trivial extensions

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.