Address.
Department of Differential Equations,
Faculty of Mathematics and Informatics,
University Transilvania of Brasov, 2200 Brasov,
Romania
E-mail. cciupala@yahoo.com
Abstract.
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.
AMSclassification. 81R60, 16W99, 53C04.
Keywords. Noncommutative geometry, almost commutative algebra, linear connections, quantum hyperplane.