Matrix Groups: An Introduction to Lie Group Theory

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Springer Science & Business Media, 2002 - Mathematics - 330 pages
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Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.
The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.
Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.
  

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Contents

II
3
III
5
IV
12
V
15
VI
18
VII
29
VIII
31
IX
33
XL
187
XLI
189
XLII
193
XLIII
199
XLIV
203
XLV
211
XLVI
215
XLVII
217

X
37
XI
45
XII
51
XIII
55
XIV
56
XV
59
XVI
67
XVII
71
XVIII
76
XIX
84
XX
86
XXI
92
XXII
99
XXIII
111
XXIV
113
XXV
116
XXVI
120
XXVII
122
XXVIII
129
XXIX
130
XXX
139
XXXI
143
XXXII
151
XXXIII
152
XXXIV
157
XXXV
165
XXXVI
171
XXXVII
179
XXXVIII
181
XXXIX
183
XLVIII
222
XLIX
224
L
226
LI
227
LII
229
LIII
235
LIV
238
LV
241
LVI
244
LVII
249
LVIII
251
LIX
255
LX
259
LXI
263
LXII
267
LXIII
270
LXIV
272
LXV
276
LXVI
278
LXVII
289
LXVIII
291
LXIX
293
LXX
297
LXXI
298
LXXII
299
LXXIII
303
LXXIV
323
LXXV
325
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About the author (2002)

Alan Baker, FRS, is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. He has received numerous international awards, including, in 1970, a Fields medal for his work in number theory. This is his third authored book: he has edited four others for publication.

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