English

Noncommutative epsilon-graded connections

Mathematical Physics 2013-01-31 v2 High Energy Physics - Theory math.MP Quantum Algebra Rings and Algebras

Abstract

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

Keywords

Cite

@article{arxiv.0811.3567,
  title  = {Noncommutative epsilon-graded connections},
  author = {Axel de Goursac and Thierry Masson and Jean-Christophe Wallet},
  journal= {arXiv preprint arXiv:0811.3567},
  year   = {2013}
}

Comments

37 pages

R2 v1 2026-06-21T11:44:06.093Z