INTEGRAL BASES FOR AFFINE LIE ALGEBRAS
AND THEIR UNIVERSAL ENVELOPING ALGEBRAS
David Mitzman
1
1. INTRODUCTION
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 [19], [20] and [15]). In addition, some recent general
references on Kac-Moody Lie algebras are [6], [9], [17], [23]. 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.
If
A is an algebra
(or Lie algebra) over lF, then an integral form for A is an algebra
(or Lie algebra) All. over
71.
(in the obvious sense) such that
A71. @ll.lF
=
A.
Integral forms for finite-dimensional semisimple Lie algebras were
first constructed and studied by Chevalley [3]. They provide the
1980 Mathematics Subject Classification. 17B65, 17B35, 17B20, 17B05.
1This
work is a revised version of the author's Ph.D. thesis
written under the supervision of
J.
Lepowsky at Rutgers University, 1983.
The author was partially supported by a Graduate Research Fellowship
from
Rut~ers
University.
1
http://dx.doi.org/10.1090/conm/040
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