Geodesic
Differential calculus on almost commutative algebras and applications to the quantum hyperplane
Archivum mathematicum, Tome 41 (2005) no. 4, pp. 359-377.

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In this paper we introduce a new class of differential graded algebras named DG $\rho $-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 $\rho $-algebra. Then we introduce linear connections on a $\rho $-bimodule $M$ over a $\rho $-algebra $A$ and extend these connections to the space of forms from $A$ to $M$. We apply these notions to the quantum hyperplane.
Classification : 16E45, 16W35, 16W50, 58C50, 81R60
Keywords: noncommutative geometry; almost commutative algebra; linear connections; quantum hyperplane 
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     title = {Differential calculus on almost commutative algebras and applications to the quantum hyperplane},
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Ciupală, Cătălin. Differential calculus on almost commutative algebras and applications to the quantum hyperplane. Archivum mathematicum, Tome 41 (2005) no. 4, pp. 359-377. http://geodesic.mathdoc.fr/item/ARM_2005__41_4_a1/