04020nam 22005293 450 991097082490332120231110230402.097814704653221470465329(CKB)4100000011975390(MiAaPQ)EBC6661103(Au-PeEL)EBL6661103(OCoLC)1259589112(RPAM)22488161(EXLCZ)99410000001197539020210901d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGalois and Cleft Monoidal Cowreaths. Applications1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (145 pages)Memoirs of the American Mathematical Society ;v.2709781470447526 1470447525 Includes bibliographical references.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."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"--Provided by publisher.Memoirs of the American Mathematical Society Galois theoryHopf algebrasGalois theory.Hopf algebras.512/.32Bulacu D1801285Torrecillas B1801286MiAaPQMiAaPQMiAaPQBOOK9910970824903321Galois and Cleft Monoidal Cowreaths. Applications4346424UNINA01083nas 2200385 c 450 991089645480332120241113203347.0(DE-599)ZDB2581382-1(OCoLC)1368944735(DE-101)1008248762(CKB)5710000000107647(EXLCZ)99571000000010764720101111b18191819 |y |gerur|||||||||||txtrdacontentcrdamediacrrdacarrierThemiswissenschaftliche Zeitschrift theologischen, juristischen und politischen Inhalts, für Leser jeden Standesvon Georg Heinrich von DeynJenaExpedition der Themis1819JenaAugust Schmid1819Online-RessourceGesehen am 21.06.2022ThemisZeitschriftgnd-content2003203400027DE-1019999JOURNAL9910896454803321Themis769408UNINA