Consider a dg-algebra $A$, is there any way I can estimate the Hochschild dimension, or global dimension of $A$?
More precisely the algebra that I am considering is the Endomorphism dg-algebra $\mathrm{Hom^*\left(G,G\right)}$ with $G$ a generator of the derived category of a degree $d$ hypersurface in $\mathbb{P}^n$ ( $G:=\bigoplus \mathcal{O}\left(i\right)$ as that gives control of the $\mathrm{Ext}$-spaces). If $A$ is concentrated in degree 0 I know I could argue via composition length. However, this will not work on the dg level I fear.
So I wanted to ask if anyone could help me with a reference respectively some insights on how I could handle this problem.
