Bimodule herds
| dc.creator | Brzezinski, Tomasz | |
| dc.creator | Vercruysse, Joost | |
| dc.date | 2008-05-16 | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:13Z | |
| dc.date.available | 2026-07-07T09:43:13Z | |
| dc.description | The notion of a bimodule herd is introduced and studied. A bimodule herd consists of a $B$-$A$ bimodule, its formal dual, called a pen, and a map, called a shepherd, which satisfies untiality and coassociativity conditions. It is shown that every bimodule herd gives rise to a pair of corings and coactions. If, in addition, a bimodule herd is tame i.e. it is faithfully flat and a progenerator, then these corings are associated to entwining structures; the bimodule herd is a Galois comodule of these corings. The notion of a bicomodule coherd is introduced as a formal dualisation of the definition of a bimodule herd. Every bicomodule coherd defines a pair of (non-unital) rings. It is shown that a tame $B$-$A$ bimodule herd defines a bicomodule coherd, and sufficient conditions for the derived rings to be isomorphic to $A$ and $B$ are discussed. The composition of bimodule herds via the tensor product is outlined. The notion of a bimodule herd is illustrated by the example of Galois co-objects of a commutative, faithfully flat Hopf algebra. | |
| dc.description | 34 pages; v.2: main theorems reformulated, references added | |
| dc.identifier | https://arxiv.org/abs/0805.2510 | |
| dc.identifier | http://arxiv.org/abs/0805.2510 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162473 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30; 16W35 | |
| dc.title | Bimodule herds | |
| dc.type | text |