  Given a connected non-negative unit form we construct an extended affine Lie
algebra by giving a Chevalley basis for it. We also obtain this algebra as a
quotient of an algebra defined by means of generalized Serre relations by M.
Barot, D. Kussin and H. Lenzing. This is done in an analogous way to the
construction of the simply-laced affine Kac-Moody algebras. Thus, we obtain a
family of extended affine Lie algebras of simply-laced Dynkin type and
arbitrary nullity. Furthermore, there is a one-to-one correspondence between
these Lie algebras and the equivalence classes of connected non-negative unit
forms.
