INTEGRAL BASES FOR AFFINE LIE ALGEBRAS
AND THEIR UNIVERSAL ENVELOPING ALGEBRAS
During the past ten years the field of Kac-Moody Lie algebras has
experienced enormous growth and development. Interesting accounts of
this development have recently been given by two protagonists in the
field (see ,  and ). In addition, some recent general
references on Kac-Moody Lie algebras are , , , . To
place the present work in its context we briefly review the relevant
background in the theories of semisimple and Kac-Moody Lie algebras.
Let lF denote a field of characteristic 0.
A is an algebra
(or Lie algebra) over lF, then an integral form for A is an algebra
(or Lie algebra) All. over
(in the obvious sense) such that
Integral forms for finite-dimensional semisimple Lie algebras were
first constructed and studied by Chevalley . They provide the
1980 Mathematics Subject Classification. 17B65, 17B35, 17B20, 17B05.
work is a revised version of the author's Ph.D. thesis
written under the supervision of
Lepowsky at Rutgers University, 1983.
The author was partially supported by a Graduate Research Fellowship