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

BERLIN SPRINGER, R.W. Carter, Алексей Иванович Кострикин, V.P. Platonov

Springer Science & Business Media, 1996 - Mathematics - 239 pages

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.

Contents

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

About the author

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.

Bibliographic information

• Title: Algebra IX: Finite Groups of Lie Type. Finite-Dimensional Division Algebras; Encyclopaedia of Mathematical Sciences, ISSN 0938-0396
• Authors: BERLIN SPRINGER, R.W. Carter, Алексей Иванович Кострикин, V.P. Platonov
• Editors: Алексей Иванович Кострикин, I.R. Shafarevich, R. V. Gamkrelidze
• Translated by: P.M. Cohn
• Contributors: Igor R. Xafarevitx, A. N. Parshin, V.I. Yanchevskii
• Edition: illustrated
• Publisher: Springer Science & Business Media, 1996
• ISBN: 3540570381, 9783540570387
• Length: 239 pages
• Subjects: Mathematics / Algebra / Abstract; Mathematics / Algebra / General; Mathematics / Geometry / Algebraic; Mathematics / Group Theory; Mathematics / Number Theory; Mathematics / Topology