2012/01/10 by Michel Dubois-Violette, Dubois-Violette, Michel, Giovanni Landi +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #gr-qc #hep-th #math-ph #math.MP #math.QA #math.RA
paper · pdf · doi:10.48550/arxiv.1201.2040
28 pages. Significant modifications. To appear in Commun. Math. Phys
arxiv created 2013/12/03 · arxiv updated 2013/12/04
We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra \mathfrak g in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra \mathcal H in a graded differential algebra Ω which is refered to as a \mathcal 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(\mathcal H) of the Hopf algebra \mathcal H is the universal initial object of the category of \mathcal H-operations with connections.