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.
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