Let $k=\mathbb{C}$ be a field of complex number. I conider a (DG)algebra $A:=k[x]/(x^2)$ such that $\deg(x)=-1$. My question is how to compute the periodic cyclic homology, hochschild homology and hochschild cohomology of this (DG)algebra? There are some references on computing those (co)homology of the ring of dual numbers $k[x]/(x^2)$. But in my case, $\deg(x)=-1$. Is there any reference on such computations?

Let $k=\mathbb{C}$ be the field of complex numbers. I consider the (DG) algebra $A:=k[x]/(x^2)$ such that $\deg(x)=-1$. My question is how to compute the periodic cyclic homology, Hochschild homology and Hochschild cohomology of this (DG) algebra? There are some references on computing those (co)homology of the ring of dual numbers $k[x]/(x^2)$. But in my case, $\deg(x)=-1$. Is there any reference on such computations?

Let $k=\mathbb{C}$ be a field of complex number. I conider a (DG)algebra $A:=k[x]/(x^2)$ such that $deg(x)=-1$. My question is how to compute the periodic cyclic homology, hochschild homology and hochschild cohomology of this (DG)algebra? There are some references on computing those (co)homology of the ring of dual numbers $k[x]/(x^2)$. But in my case, $deg(x)=-1$. Is there any reference on such computations?

Let $k=\mathbb{C}$ be a field of complex number. I conider a (DG)algebra $A:=k[x]/(x^2)$ such that $\deg(x)=-1$. My question is how to compute the periodic cyclic homology, hochschild homology and hochschild cohomology of this (DG)algebra? There are some references on computing those (co)homology of the ring of dual numbers $k[x]/(x^2)$. But in my case, $\deg(x)=-1$. Is there any reference on such computations?