  We consider algebras over a field $k$ of characteristic zero. The article is
concerned with the isomorphism of graded vectorspaces \[ H(\gl(A))\iso\wedge
(HC(A)[-1]) \] between the Lie algebra homology of matrices and the free graded
commutative algebra on the cyclic homology of the $k$-algebra $A$, shifted down
one degree. For unital algebras this isomorphism is a classical result obtained
by Loday and Quillen and independently by Tsygan. For $H$-unital algebras, it
is known to hold too, as is that the proof follows from results of Hanlon's.
However, to our knowledge, the proof is not immediate, and has not been
published. In this paper we fill this gap in the literature by offering a
detailed proof. Moreover we establish the isomorphism in the general setting of
($H$-unital) pro-algebras.
