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EnglishWe generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra g in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra H in a graded differential algebra Ω which is refered to as a H-operation. We then generalize for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra: The Weil algebra W(H) of the Hopf algebra H is the universal initial object of the category of H-operations with connections.
| Titolo: | The Weil Algebra of a Hopf Algebra - I - A noncommutative framework | |
| Autori: | ||
| Data di pubblicazione: | 2014 | |
| Rivista: | ||
| Abstract: | We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra g in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra H in a graded differential algebra Ω which is refered to as a H-operation. We then generalize for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra: The Weil algebra W(H) of the Hopf algebra H is the universal initial object of the category of H-operations with connections. | |
| Handle: | http://hdl.handle.net/11368/2829621 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00220-014-1902-7 | |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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