Galois and Cleft Monoidal Cowreaths. Applications
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| Autore: |
Bulacu D
|
| Titolo: |
Galois and Cleft Monoidal Cowreaths. Applications
|
| Pubblicazione: | Providence : , : American Mathematical Society, , 2021 |
| ©2021 | |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (145 pages) |
| Disciplina: | 512/.32 |
| Soggetto topico: | Galois theory |
| Hopf algebras | |
| Altri autori: |
TorrecillasB
|
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | Cover -- Title page -- Part 1. Introduction and Preliminaries -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Coflat and robust objects -- 2.2. Cowreaths in monoidal categories and entwined module categories associated to them -- Part 2. A Schneider type theorem for monoidal cowreaths -- Chapter 3. A pair of adjoint functors -- Chapter 4. The fundamental theorem for entwined modules over monoidal cowreaths -- Chapter 5. Total integrals and the structure theorem -- Part 3. Cleft cowreaths and wreath algebras -- Chapter 6. Cleft cowreaths -- Chapter 7. Cleft cowreaths versus wreath algebras -- Part 4. Applications -- Chapter 8. Cleft (co)wreaths arising from Doi-Hopf modules over (quasi-)bialgebras -- Chapter 9. Cleft (co)wreaths arising from crossed products by a coalgebra -- Chapter 10. Cleft (co)wreaths arising from -Doi-Hopf cowreaths -- Chapter 11. Cleft (co)wreaths arising from generalized crossed products -- Chapter 12. Cleft (co)wreaths arising from quasi-Hopf bimodules -- Bibliography -- Back Cover. |
| Sommario/riassunto: | "We introduce (pre-)Galois and cleft monoidal cowreaths. Generalizing a result of Schneider, to any pre-Galois cowreath we associate a pair of adjoint functors L R and give necessary and sufficient conditions for the adjunction to be an equivalence of categories. Inspired by the work of Doi we also give sufficient conditions for L R to be an equivalence, and consequently conditions under which a fundamental structure theorem for entwined modules over monoidal cowreaths holds. We show that a cowreath is cleft if and only if it is Galois and has the normal basis property; this generalizes a result concerning Hopf cleft extensions due to Doi and Takeuchi. Furthermore, we show that the cleft cowreaths are in a one to one correspondence with what we call cleft wreaths. The latter are wreaths in the sense of Lack and Street, equipped with two additional morphisms satisfying some compatibility relations. Note that, in general, the algebras defined by cleft wreaths cannot be identified to (generalized) crossed product algebras, as they were defined by Doi and Takeuchi, and Blattner, Cohen and Montgomery. This becomes more transparent when we apply our theory to cowreaths defined by actions and coactions of a quasi-Hopf algebra, monoidal entwining structures and Doi-Hopf structures, respectively. In particular, we obtain that some constructions of Brzezinski and Schauenburg produce examples of cleft wreaths, and therefore of cleft cowreaths, too"-- |
| Titolo autorizzato: | Galois and Cleft Monoidal Cowreaths. Applications |
| ISBN: | 9781470465322 |
| 1470465329 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910970824903321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society