John Stillwell - Naive Lie Theory.pdf - Index of

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206 Bibliography Otto Schreier. Abstrakte kontinuierliche Gruppen. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 4:15–32, 1925. Otto Schreier. Die Verwandtschaft stetiger Gruppen im Grossen. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 5: 233–244, 1927. Jean-Pierre Serre. Lie Algebras and Lie Groups. W.A.Benjamin,Inc., New York–Amsterdam, 1965. K. Tapp. Matrix Groups for Undergraduates. American Mathematical Society, Providence, RI, 2005. Thomas M. Thompson. From Error-Correcting Codes through Sphere Packings to Simple Groups. Mathematical Association of America, Washington, DC, 1983. John von Neumann. Über die analytischen Eigenschaften von Gruppen linearer Transformationen und ihrer Darstellungen. Mathematische Zeitschrift, 30:3–42, 1929. J. H. M. Wedderburn. The absolute value of the product of two matrices. Bulletin of the American Mathematical Society, 31:304–308, 1925. Hermann Weyl. Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen. I. Mathematische Zeitschrift, 23:271–301, 1925. Hermann Weyl. The Classical Groups. Their Invariants and Representations. Princeton University Press, Princeton, N.J., 1939.
Index 24-cell, 36 A 5 , 45, 202 A n , 45, 202 abelian group, 24, 41, 60 maximal, 66 absolute value and determinant, 5 as distance, 7, 161 multiplicative property, 6 of complex numbers, 5 of matrices, 84 submultiplicative property, 84 Adams, J. Frank, 202 addition formula, 76, 96, 100, 141 additive notation, 24 Ado, I. D., 72, 105, 113 Aff(1), 87 is noncompact, 88 is not closed, 165 is not simple, 88 Lie algebra of, 89 affine transformations, 87 almost simple, 72, 115 angle, 49 antipodal, 15, 33, 118, 189, 190 antisymmetric property, 13 automorphism, 44 axis of rotation, 14, 17 Baker, H. F., 153 Berger, Marcel, 47 bilinearity, 81, 83, 108 Birkhoff, Garrett, 72 block multiplication, 41, 58, 59 Bombelli, Rafael, 19 Bourbaki, Nicolas, 159 Brouwer, L. E. J., 149 Campbell, J. E., 153 Cardano, Girolamo, 19 Cartan, Élie, 37, 45, 73, 115, 137, 202 Cartan–Dieudonné theorem, 37 Cauchy–Schwarz inequality, 84, 85 proof, 86 Cayley, Arthur, 10, 21 center, 48, 61, 115 and normal subgroups, 69 and path-connectedness, 69 of a Lie group, 115 of GL(n,C), 111 of SL(n,C), 111 of SO(2m), 67 of SO(2m + 1),68 of SO(3), 61, 151 of Sp(n), 68 of SU(n), 68 of U(n), 68 Chevalley, Claude, 71, 113 closed interval, 163 matrix group, 143 path, 178, 184 set, 160 definition, 162 subgroups, 160 closure, 163 commutative law, 6 commutator, 105 compactness, 88, 160 207
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Undergraduate Texts in Mathematics
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John Stillwell Naive Lie Theory 123
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To Paul Halmos In Memoriam
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viii Preface Where my book diverges
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Contents 1 Geometry of complex numb
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Contents xiii 8 Topology 160 8.1 Op
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2 1 The geometry of complex numbers
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10 1 The geometry of complex number
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24 2 Groups 2.1 Crash course on gro
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26 2 Groups This algebraic argument
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28 2 Groups is the right coset of H
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30 2 Groups and h ∈ ker ϕ ⇒ ϕ
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32 2 Groups show that the real proj
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34 2 Groups R Q α/2 θ/2 α/2 P Fi
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36 2 Groups 1/2 turn 1/3 turn Figur
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38 2 Groups 2.4.4 Show that reflect
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40 2 Groups 2.5.1 Check that q ↦
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42 2 Groups Exercises If we let x 1
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44 2 Groups SO(4) is not simple. Th
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46 2 Groups include “infinitesima
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3 Generalized rotation groups PREVI
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50 3 Generalized rotation groups Th
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52 3 Generalized rotation groups An
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54 3 Generalized rotation groups th
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56 3 Generalized rotation groups Pa
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58 3 Generalized rotation groups Ho
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60 3 Generalized rotation groups On
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62 3 Generalized rotation groups Ex
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64 3 Generalized rotation groups In
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66 3 Generalized rotation groups Th
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68 3 Generalized rotation groups Ca
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70 3 Generalized rotation groups Pr
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72 3 Generalized rotation groups Ma
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4 The exponential map PREVIEW The g
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76 4 The exponential map course, th
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78 4 The exponential map imaginary
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80 4 The exponential map This const
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82 4 The exponential map 4.4 The Li
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84 4 The exponential map 4.5 The ex
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86 4 The exponential map Definition
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88 4 The exponential map obtained b
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90 4 The exponential map Then subst
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92 4 The exponential map It was dis
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94 5 The tangent space 5.1 Tangent
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96 5 The tangent space The matrices
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98 5 The tangent space as in ordina
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100 5 The tangent space Conversely,
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102 5 The tangent space Exercises A
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104 5 The tangent space To see why
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106 5 The tangent space 5.5 Dimensi
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108 5 The tangent space but not nec
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110 5 The tangent space Conversely,
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112 5 The tangent space However, th
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114 5 The tangent space the set of
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6 Structure of Lie algebras PREVIEW
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118 6 Structure of Lie algebras isa
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120 6 Structure of Lie algebras An
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122 6 Structure of Lie algebras 6.3
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124 6 Structure of Lie algebras We
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126 6 Structure of Lie algebras whi
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128 6 Structure of Lie algebras Our
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130 6 Structure of Lie algebras [X,
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132 6 Structure of Lie algebras l
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134 6 Structure of Lie algebras and
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136 6 Structure of Lie algebras If
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138 6 Structure of Lie algebras of
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140 7 The matrix logarithm 7.1 Loga
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142 7 The matrix logarithm 7.1.1 Su
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144 7 The matrix logarithm Taking e
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146 7 The matrix logarithm If A(t)
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148 7 The matrix logarithm The log
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150 7 The matrix logarithm 7.4.1 Sh
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152 7 The matrix logarithm By the t
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154 7 The matrix logarithm The idea
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Page 216 and 217: Bibliography J. Frank Adams. Lectur
Page 220 and 221: 208 Index and continuity, 171 and u
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Page 228 and 229: 216 Index is semisimple, 47 so(4) i
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