On modules associated to coalgebra Galois extensions
| dc.creator | Brzezinski, Tomasz | |
| dc.date | 1997-12-09 | |
| dc.date | 1998-10-09 | |
| dc.date.accessioned | 2026-07-07T05:57:45Z | |
| dc.date.available | 2026-07-07T05:57:45Z | |
| dc.description | For a given entwining structure $(A,C)_ψ$ involving an algebra $A$, a coalgebra $C$, and an entwining map $ψ: C\otimes A\to A\otimes C$, a category $\M_A^C(ψ)$ of right $(A,C)_ψ$-modules is defined and its structure analysed. In particular, the notion of a measuring of $(A,C)_ψ$ to $(\tA,\tC)_\tpsi$ is introduced, and certain functors between $\M_A^C(ψ)$ and $\M_\tA^\tC(\tpsi)$ induced by such a measuring are defined. It is shown that these functors are inverse equivalences iff they are exact (or one of them faithfully exact) and the measuring satisfies a certain Galois-type condition. Next, left modules $E$ and right modules $\bar{E}$ associated to a $C$-Galois extension $A$ of $B$ are defined. These can be thought of as objects dual to fibre bundles with coalgebra $C$ in the place of a structure group, and a fibre $V$. Cross-sections of such associated modules are defined as module maps $E\to B$ or $\bar{E}\to B$. It is shown that they can be identified with suitably equivariant maps from the fibre to $A$. Also, it is shown that a $C$-Galois extension is cleft if and only if $A=B\tens C$ as left $B$-modules and right $C$-comodules. The relationship between the modules $E$ and $\bar{E}$ is studied in the case when $V$ is finite-dimensional and in the case when the canonical entwining map is bijective. | |
| dc.description | 31 pages, LaTeX, uses amscd and amssymb. Some changes in Section 3. Version to appear in J. Algebra | |
| dc.identifier | https://arxiv.org/abs/q-alg/9712023 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9712023 | |
| dc.identifier | J. Algebra, 215:290-317, 1999 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88102 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30; 17B37; 81R50 | |
| dc.title | On modules associated to coalgebra Galois extensions | |
| dc.type | text |