Twisting all the way: from algebras to morphisms and connections
| Autor: | Aschieri, Paolo |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Int. Jou. Mod. Phys. Conf. Ser. 13 (2012) 1-19 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S201019451200668X |
| Popis: | Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (deform) H to H^F, A to A_\star and correspondingly the category of left H-modules and A-bimodules to the category of left H^F-modules and A_\star-bimodules. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A_\star-bimodule connections. Their curvatures and those on tensor product modules are also determined. Comment: 15 pages. Proceedings of the Julius Wess 2001 workshop of the Balkan Summer Institute 2011, 27-28.8.2011 Donji Milanovac, Serbia |
| Databáze: | arXiv |
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