Hochschild Cohomology of a Sullivan Algebra

Let A=(∧V,d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A= (\land V, d)}$$\end{document} be a minimal Sullivan algebra where V is finite dimensional. We show that the Hochschild cohomology HH*(A; A) can be computed in terms of derivations of A. This provides another method to compute the loop space homology of a simply connected space for which π∗(X)⊗Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ \pi_*(X) \otimes \mathbb{Q} }$$\end{document} is finite dimensional.