3 citations · 5 across the 8 of their papers we have counts for
8 papers · 1 filter
The structure of weak coalgebra-Galois extensions
Tomasz Brzezinski, Ryan B. Turner, Adam P. Wrightson
Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, th…
Yang-Baxter Systems and Entwining Structures
Tomasz Brzezinski, Florin F. Nichita
It is shown that a Yang-Baxter system can be constructed from any entwining structure. It is also shown that, conversely, Yang-Baxter systems of certain type lead to entwining stru…
Non-commutative 4-spheres based on all Podleś 2-spheres and beyond
Tomasz Brzezinski, Cezary Gonera
A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described. For each such space a noncommut…
Doi-Koppinen modules for quantum groupoids
Tomasz Brzezinski, Stefaan Caenepeel, Gigel Militaru
A definition of a Doi-Koppinen datum over a noncommutative algebra is proposed. The idea is to replace a bialgebra in a standard Doi-Koppinen datum with a bialgebroid. The correspo…
Bialgebroids, -bialgebras and duality
Tomasz Brzezinski, Gigel Militaru
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's -bialgebras is explicitly proven. A new class of examples of bialgebroids is c…
Coalgebra-Galois extensions from the extension theory point of view
Tomasz Brzezinski
Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a s…