Let $X$ be a simply connected rational elliptic space of formal dimension $n$ and let $\E(X)$ denote the group of homotopy classes of self-equivalences of $X$. If $X^{ [k]}$ denotes the $k^{ \text{ th}}$ Postikov section of $X$ and $X^{ k}$ denotes its $k^{ \text{ th}}$ skeleton, then making use of the models of Sullivan and Quillen we prove that $\E(X)\cong\E(X^{ [n]})$ and if $n>m=max\big\{ k \,| \,\pi_{ k}(X)\neq 0\big\}$ and $\E(X)$ is finite, then $\E(X)\cong\E(X^{ m+1})$. Moreover, in case when $X$ is 2-connected, we show that if $\pi_{ n}(X)\neq0$, then the group $\E(X)$ is infinite.
Categories: math.AT