3 D Points Times Calabi - Yau Algebraic Loop Homology

This Master degree thesis mainly concerns the calculation of the Hochschild homology and cyclic homologyof3-dimensional Calabi-Yau algebras. We gener-alize the method of Van den Bergh and consider a class of AS-regular algebra as the deformation of a polynomial Poisson algebra. Here the corresponding Poisson bracket produces a non-regular sequences, we use the technique inspired from [BP] to calculate the Poisson homology and then compute the Hochschild homology of3-dimensional Calabi-Yau algebra of type (1331)-S1’.