Algebra IX: Finite Groups of Lie Type. Finite-Dimensional Division Algebras

Front Cover
The finite groups of Lie type are of central mathematical importance and the problem of understanding their irreducible representations is of great interest. The representation theory of these groups over an algebraically closed field of characteristic zero was developed by P.Deligne and G.Lusztig in 1976 and subsequently in a series of papers by Lusztig culminating in his book in 1984. The purpose of the first part of this book is to give an overview of the subject, without including detailed proofs. The second part is a survey of the structure of finite-dimensional division algebras with many outline proofs, giving the basic theory and methods of construction and then goes on to a deeper analysis of division algebras over valuated fields. An account of the multiplicative structure and reduced K-theory presents recent work on the subject, including that of the authors. Thus it forms a convenient and very readable introduction to a field which in the last two decades has seen much progress.
 

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Contents

I
3
III
6
IV
7
V
12
VI
12
VII
15
VIII
18
X
20
LXXXVIII
144
XC
145
XCII
146
XCIII
147
XCIV
149
XCV
151
XCVII
153
XCVIII
154

XI
21
XII
23
XIII
25
XIV
27
XV
28
XVI
29
XVIII
30
XIX
32
XX
34
XXI
36
XXII
38
XXIII
39
XXIV
42
XXV
44
XXVII
46
XXVIII
47
XXIX
48
XXXI
50
XXXII
51
XXXIII
53
XXXIV
58
XXXVI
61
XXXVIII
63
XXXIX
66
XL
71
XLI
74
XLII
78
XLIII
81
XLIV
84
XLV
86
XLVI
87
XLVII
91
XLVIII
95
XLIX
98
LI
99
LII
101
LIII
103
LIV
109
LV
123
LVI
125
LVII
126
LIX
127
LX
128
LXI
131
LXII
132
LXIV
133
LXVII
134
LXX
135
LXXIII
136
LXXV
137
LXXVI
138
LXXVIII
139
LXXX
140
LXXXV
142
LXXXVII
143
XCIX
155
C
156
CII
157
CIII
159
CV
161
CVI
162
CVII
163
CIX
164
CX
165
CXI
166
CXII
167
CXIII
168
CXIV
169
CXV
170
CXVII
171
CXIX
172
CXXI
173
CXXIII
174
CXXIV
175
CXXV
176
CXXVIII
179
CXXIX
180
CXXX
182
CXXXI
183
CXXXII
184
CXXXIII
185
CXXXIV
186
CXXXVI
187
CXXXVIII
188
CXL
189
CXLIII
190
CXLVI
191
CXLIX
193
CLI
195
CLII
196
CLIV
197
CLVI
200
CLVII
205
CLIX
206
CLXI
207
CLXII
208
CLXIII
209
CLXVI
210
CLXVII
211
CLXVIII
212
CLXX
213
CLXXI
214
CLXXII
215
CLXXIII
216
CLXXIV
218
CLXXV
219
CLXXVI
221
CLXXVII
222
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About the author (1996)

Igor Rostislavovich Shafarevich was born in Zhitomir, Ukraine on June 3, 1923. He graduated from Moscow State University with a specialty in astronomy. He taught at Moscow State University for more than 30 years. He was an internationally renowned mathematician who played a central role in the anti-Soviet dissident movement during the Cold War. His textbooks on algebraic geometry were translated into English and regarded as classics in the field. He also wrote The Socialist Phenomenon and contributed essays to From Under the Rubble. He died on February 19, 2017 at the age of 93.

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