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1
Content available remote

A note on flat noncommutative connections

100%
Brzeziński T.
Banach Center Publications
|
2012
|
tom 98
|
nr 1
43-53
EN
It is proven that every flat connection or covariant derivative ∇ on a left A-module M (with respect to the universal differential calculus) induces a right A-module structure on M so that ∇ is a bimodule connection on M or M is a flat differentiable bimodule. Similarly a flat hom-connection on a right A-module M induces a compatible left A-action.
2
Content available remote

The structure of corings with a grouplike element

100%
Brzeziński T.
Banach Center Publications
|
2003
|
tom 61
|
nr 1
21-35
EN
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.
3
Content available remote

Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two

100%
Brzeziński T.
Colloquium Mathematicum
|
2015
|
tom 139
|
nr 1
111-119
EN
Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.
4
Content available remote

Quantum Fibre Bundles. An Introduction

100%
Brzeziński T.
Banach Center Publications
|
1997
|
tom 39
|
nr 1
211-223
EN
An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.
5
Content available remote

A note on coalgebra gauge theory

100%
Brzeziński T.
Banach Center Publications
|
1997
|
tom 40
|
nr 1
289-292
EN
A generalisation of quantum principal bundles in which a quantum structure group is replaced by a coalgebra is proposed.
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