  Let M be a simply-connected closed oriented N-dimensional manifold. We prove
that for any field of coefficients there exists a natural homomorphism of
commutative graded algebras $\Psi : H_\ast (\Omega {aut}_1 M) \to H_{\ast
+N}(M^{S^1})$ where $H_\ast (M^{S^1})$ is the loop algebra defined by
Chas-Sullivan. As usual ${aut}_1 X$ (resp. $\Omega X$) denotes the monoid of
the self-equivalences homotopic to the identity map (resp. the space of based
loops) of the space X. Moreover, if $\bk$ is of characteristic zero, $\Psi$
yields isomorphisms $\pi_n(\Omega {aut}_1 M) \otimes \bk \cong \hH^{n+N}_{(1)}$
where $\displaystyle \oplus_{l=1}^\infty \hH^n_{(l)}$ denotes the Hodge
decomposition on $H^\ast (M ^{S^1})$.
