Central extensions of generalized Kac-Moody algebras
Richard Borcherds
J. Algebra. Vol 140 No. 2, July 1991, 330-335. 

The main result of Borcherds [1] states that graded Lie algebras with an 
``almost positive definite'' contravariant bilinear form are essentially 
the same as central extensions of generalized Kac-Moody algebras. In this 
paper we calculate these central extensions. Ordinary Kac-Moody algebras 
have nontrivial centers when the Cartan matrix is singular; generalized 
Kac-Moody algebras turn out to have some ``extra'' center in their universal 
central extensions whenever they have simple roots of multiplicity greater 
than 1, and in particular the dimension of the Cartan subalgebra can be 
larger than the number of rows of the Cartan matrix.