Noncommutative -graded connections

  • Axel de Goursac

    Laboratoire de physique théorique d'Orsay
  • Thierry Masson

    Laboratoire de physique theorique d'Orsay
  • Jean-Christophe Wallet

    Laboratoire de physique theorique d'Orsay


We introduce the new notion of -graded associative algebras which takes its roots from the notion of commutation factors introduced in the context of Lie algebras ([Scheunert, 1979]). We define and study the associated notion of -derivation-based differential calculus, which generalizes the derivation-based calculus on associative algebras. A corresponding notion of noncommutative connection is also defined. We illustrate these considerations with various examples of -graded commutative algebras, in particular some graded matrix algebras and the Moyal algebra. This last example also permits us to interpret mathematically a noncommutative gauge field theory.

Cite this article

Axel de Goursac, Thierry Masson, Jean-Christophe Wallet, Noncommutative -graded connections. J. Noncommut. Geom. 6 (2012), no. 2, pp. 343–387

DOI 10.4171/JNCG/94