Table of Contents
1.
Introduction ....••.....•.
1
2. Chevalley bases for semisimple and type 1 affine Lie
algebras of types A, D, E .
9
2.1 The construction of !(A) for A= At' Dt• Et 9
2.2 The construction of !(A) for A
=
Ail), oil), Eil). 21
2.3 The structure constants with respect to a
Chevalley basis •••••.•••....•
3. Chevalley bases for the remaining semisimple and
affine Lie algebras
3.1 Notation
3.2 The cases
B.
(j
2), C.
(j
2), F4
J - J -
3. 3 The cases
B~l)
(j
2), dl)
(j
2), F
4
(l)
J - J -
3.4 The cases
A!~) (j 2), D(Z) (j 2), E(
2)
""ZJ-1 - j+l - 6
3.5 The case Ag)
(j
~
1)
3.6 The case G
2

3.7
3.8
The case G(l)
. 2
The case 0(
3)
4
3.9 The structure constants with respect to a
Chevalley basis •••••••••.•••
4. Integral forms of enveloping algebras of affine
Lie algebras •••••.••..•.
.
.
.
29
38
38
43
53
59
65
77
85
89
96
111
4.1 Notation and preliminary lemmas 111
4.2 The integral form
!!z . . . . .
117
4.3 The proof of Theorem 4.2.6 for type 1 affine
Lie algebras . . . . . . . . . 123
4.4 The proof of Theorem 4.2.6 for affine Lie algebras
of types 2 and 3 139
Appendix 156
References 158
vii
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