We study locally finite simple Lie algebras containing a maximal toral
subalgebra and give the structure of those such algebras which are of countable
dimension with finite dimensional weight spaces.
This is an exposition in order to give an explicit way to understand (1) a
non-topological proof for an existence of a base of an affine root system, (2)
a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the
isotropic root multiplicities of those elliptic Lie algebras.
This is an exposition in order to give an explicit way to understand (1) a
non-topological proof for an existence of a base of an affine root system, (2)
a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the
isotropic root multiplicities of those elliptic Lie algebras.
Using the well-known recognition and structural theorem(s) for root-graded
Lie algebras and their universal coverings, we give a finite presentation for
the universal covering algebra of a centerless Lie torus of type
$X\not=A,C,BC$. We follow a unified approach for the types under consideration.