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Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Cătălin Ciupală — 2005

Archivum Mathematicum

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.

Hochschild and cyclic homology of $ρ$ -algebras.

Ciupală, Cătălin — 2006

APPS. Applied Sciences

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Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Hochschild and cyclic homology of ρ -algebras.

Hochschild and cyclic homology of $ρ$ -algebras.