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.

The Weil Algebra of a Hopf Algebra - I - A noncommutative framework

LANDI, GIOVANNI
2014

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2829621
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