Views
2 years ago

John Stillwell - Naive Lie Theory.pdf - Index of

John Stillwell - Naive Lie Theory.pdf - Index of

John Stillwell - Naive Lie Theory.pdf - Index

  • Page 2 and 3: Undergraduate Texts in Mathematics
  • Page 4 and 5: John Stillwell Naive Lie Theory 123
  • Page 6 and 7: To Paul Halmos In Memoriam
  • Page 8 and 9: viii Preface Where my book diverges
  • Page 10 and 11: Contents 1 Geometry of complex numb
  • Page 12 and 13: Contents xiii 8 Topology 160 8.1 Op
  • Page 14 and 15: 2 1 The geometry of complex numbers
  • Page 16 and 17: 4 1 The geometry of complex numbers
  • Page 18 and 19: 6 1 The geometry of complex numbers
  • Page 20 and 21: 8 1 The geometry of complex numbers
  • Page 22 and 23: 10 1 The geometry of complex number
  • Page 24 and 25: 12 1 The geometry of complex number
  • Page 26 and 27: 14 1 The geometry of complex number
  • Page 28 and 29: 16 1 The geometry of complex number
  • Page 30 and 31: 18 1 The geometry of complex number
  • Page 32 and 33: 20 1 The geometry of complex number
  • Page 34 and 35: 22 1 The geometry of complex number
  • Page 36 and 37: 24 2 Groups 2.1 Crash course on gro
  • Page 38 and 39: 26 2 Groups This algebraic argument
  • Page 40 and 41: 28 2 Groups is the right coset of H
  • Page 42 and 43: 30 2 Groups and h ∈ ker ϕ ⇒ ϕ
  • Page 44 and 45: 32 2 Groups show that the real proj
  • Page 46 and 47: 34 2 Groups R Q α/2 θ/2 α/2 P Fi
  • Page 48 and 49: 36 2 Groups 1/2 turn 1/3 turn Figur
  • Page 50 and 51: 38 2 Groups 2.4.4 Show that reflect
  • Page 52 and 53:

    40 2 Groups 2.5.1 Check that q ↦

  • Page 54 and 55:

    42 2 Groups Exercises If we let x 1

  • Page 56 and 57:

    44 2 Groups SO(4) is not simple. Th

  • Page 58 and 59:

    46 2 Groups include “infinitesima

  • Page 60 and 61:

    3 Generalized rotation groups PREVI

  • Page 62 and 63:

    50 3 Generalized rotation groups Th

  • Page 64 and 65:

    52 3 Generalized rotation groups An

  • Page 66 and 67:

    54 3 Generalized rotation groups th

  • Page 68 and 69:

    56 3 Generalized rotation groups Pa

  • Page 70 and 71:

    58 3 Generalized rotation groups Ho

  • Page 72 and 73:

    60 3 Generalized rotation groups On

  • Page 74 and 75:

    62 3 Generalized rotation groups Ex

  • Page 76 and 77:

    64 3 Generalized rotation groups In

  • Page 78 and 79:

    66 3 Generalized rotation groups Th

  • Page 80 and 81:

    68 3 Generalized rotation groups Ca

  • Page 82 and 83:

    70 3 Generalized rotation groups Pr

  • Page 84 and 85:

    72 3 Generalized rotation groups Ma

  • Page 86 and 87:

    4 The exponential map PREVIEW The g

  • Page 88 and 89:

    76 4 The exponential map course, th

  • Page 90 and 91:

    78 4 The exponential map imaginary

  • Page 92 and 93:

    80 4 The exponential map This const

  • Page 94 and 95:

    82 4 The exponential map 4.4 The Li

  • Page 96 and 97:

    84 4 The exponential map 4.5 The ex

  • Page 98 and 99:

    86 4 The exponential map Definition

  • Page 100 and 101:

    88 4 The exponential map obtained b

  • Page 102 and 103:

    90 4 The exponential map Then subst

  • Page 104 and 105:

    92 4 The exponential map It was dis

  • Page 106 and 107:

    94 5 The tangent space 5.1 Tangent

  • Page 108 and 109:

    96 5 The tangent space The matrices

  • Page 110 and 111:

    98 5 The tangent space as in ordina

  • Page 112 and 113:

    100 5 The tangent space Conversely,

  • Page 114 and 115:

    102 5 The tangent space Exercises A

  • Page 116 and 117:

    104 5 The tangent space To see why

  • Page 118 and 119:

    106 5 The tangent space 5.5 Dimensi

  • Page 120 and 121:

    108 5 The tangent space but not nec

  • Page 122 and 123:

    110 5 The tangent space Conversely,

  • Page 124 and 125:

    112 5 The tangent space However, th

  • Page 126 and 127:

    114 5 The tangent space the set of

  • Page 128 and 129:

    6 Structure of Lie algebras PREVIEW

  • Page 130 and 131:

    118 6 Structure of Lie algebras isa

  • Page 132 and 133:

    120 6 Structure of Lie algebras An

  • Page 134 and 135:

    122 6 Structure of Lie algebras 6.3

  • Page 136 and 137:

    124 6 Structure of Lie algebras We

  • Page 138 and 139:

    126 6 Structure of Lie algebras whi

  • Page 140 and 141:

    128 6 Structure of Lie algebras Our

  • Page 142 and 143:

    130 6 Structure of Lie algebras [X,

  • Page 144 and 145:

    132 6 Structure of Lie algebras l

  • Page 146 and 147:

    134 6 Structure of Lie algebras and

  • Page 148 and 149:

    136 6 Structure of Lie algebras If

  • Page 150 and 151:

    138 6 Structure of Lie algebras of

  • Page 152 and 153:

    140 7 The matrix logarithm 7.1 Loga

  • Page 154 and 155:

    142 7 The matrix logarithm 7.1.1 Su

  • Page 156 and 157:

    144 7 The matrix logarithm Taking e

  • Page 158 and 159:

    146 7 The matrix logarithm If A(t)

  • Page 160 and 161:

    148 7 The matrix logarithm The log

  • Page 162 and 163:

    150 7 The matrix logarithm 7.4.1 Sh

  • Page 164 and 165:

    152 7 The matrix logarithm By the t

  • Page 166 and 167:

    154 7 The matrix logarithm The idea

  • Page 168 and 169:

    156 7 The matrix logarithm Next, re

  • Page 170 and 171:

    158 7 The matrix logarithm Exercise

  • Page 172 and 173:

    8 Topology PREVIEW One of the essen

  • Page 174 and 175:

    162 8 Topology The set N ε (P) is

  • Page 176 and 177:

    164 8 Topology 8.2 Closed matrix gr

  • Page 178 and 179:

    166 8 Topology Matrix Lie groups Wi

  • Page 180 and 181:

    168 8 Topology also a continuous fu

  • Page 182 and 183:

    170 8 Topology Pick, say, the leftm

  • Page 184 and 185:

    172 8 Topology true that f −1 (

  • Page 186 and 187:

    174 8 Topology describing specific

  • Page 188 and 189:

    176 8 Topology These roots represen

  • Page 190 and 191:

    178 8 Topology The restriction of d

  • Page 192 and 193:

    180 8 Topology can divide [0,1] int

  • Page 194 and 195:

    182 8 Topology 8.8 Discussion Close

  • Page 196 and 197:

    184 8 Topology topology book will s

  • Page 198 and 199:

    9 Simply connected Lie groups PREVI

  • Page 200 and 201:

    188 9 Simply connected Lie groups T

  • Page 202 and 203:

    190 9 Simply connected Lie groups I

  • Page 204 and 205:

    192 9 Simply connected Lie groups f

  • Page 206 and 207:

    194 9 Simply connected Lie groups 9

  • Page 208 and 209:

    196 9 Simply connected Lie groups T

  • Page 210 and 211:

    198 9 Simply connected Lie groups W

  • Page 212 and 213:

    200 9 Simply connected Lie groups L

  • Page 214 and 215:

    202 9 Simply connected Lie groups L

  • Page 216 and 217:

    Bibliography J. Frank Adams. Lectur

  • Page 218 and 219:

    206 Bibliography Otto Schreier. Abs

  • Page 220 and 221:

    208 Index and continuity, 171 and u

  • Page 222 and 223:

    210 Index Lorentz, 113 matrix, vii,

  • Page 224 and 225:

    212 Index knew SO(4) anomaly, 47 Tr

  • Page 226 and 227:

    214 Index projective space, 185 rea

  • Page 228 and 229:

    216 Index is semisimple, 47 so(4) i

  • Page 230:

    Undergraduate Texts in Mathematics

Lie Groups, Lie Algebras and the Exponential Map
math.columbia.edu
A Linear Algebraic Approach to Quaternions - Geometric Tools
geometrictools.com
MAT 610: Numerical Linear Algebra - Index of
usm.edu