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.



Titolo: The Weil Algebra of a Hopf Algebra - I - A noncommutative framework
Autori: 
LANDI, GIOVANNI
mostra contributor esterni 
Data di pubblicazione: 2014
Rivista: 
COMMUNICATIONS IN MATHEMATICAL PHYSICS  
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): 10.1007/s00220-014-1902-7
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