Linear connections on almost commutative algebras.

Ciupală, C.

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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.