Noncommutative epsilon-graded connections

Details Noncommutative epsilon-graded connections Noncommutative epsilon-graded connections

2008-11-21

arxiv.org/abs/0811.3567v2

J. Noncommut. Geom. 6: 343-387, 2012

Physics

Mathematical Physics

37 pages

Scientific paper

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.

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