  We investigate a class of Kac-Moody algebras previously not considered. We
refer to them as n-extended Lorentzian Kac-Moody algebras defined by their
Dynkin diagrams through the connection of an $A_n$ Dynkin diagram to the node
corresponding to the affine root. The cases $n=1$ and $n=2$ correspond to the
well studied over and very extended Kac-Moody algebras, respectively, of which
the particular examples of $E_{10}$ and $E_{11}$ play a prominent role in
string and M-theory. We construct closed generic expressions for their
associated roots, fundamental weights and Weyl vectors. We use these quantities
to calculate specific constants from which the nodes can be determined that
when deleted decompose the n-extended Lorentzian Kac-Moody algebras into simple
Lie algebras and Lorentzian Kac-Moody algebra. The signature of these constants
also serves to establish whether the algebras possess $SO(1,2)$ and/or
$SO(3)$-principal subalgebras.
