Differential calculus on almost commutative algebras and applications to the quantum hyperplane
In this paper we introduce a new class of differential graded algebras named DG -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a -algebra. Then we introduce linear connections on a -bimodule over a -algebra and extend these connections to the space of forms from to . We apply these notions to the quantum hyperplane.