In this paper we introduce a new class of differential graded algebras named DG ρ-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 ρ-algebra. Then we introduce linear connections on a ρ-bimodule M over a ρ-algebra A and extend these connections to the space of forms from A to M. We apply these notions to the quantum hyperplane.
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