John Stillwell - Naive Lie Theory.pdf - Index of

More documents

Recommendations

Info

Bibliography J. Frank Adams. Lectures on Lie Groups. W.A.Benjamin,Inc.,New York–Amsterdam, 1969. Marcel Berger. Geometry. I. Springer-Verlag, Berlin, 1987. Garrett Birkhoff. Lie groups simply isomorphic to no linear group. Bulletin of the American Mathematical Society, 42:883–888, 1936. N. Bourbaki. Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie. Hermann, Paris, 1972. L. E. J. Brouwer. Beweis der Invarianz der Dimensionenzahl. Mathematische Annalen, 71:161–165, 1911. Élie Cartan. Nombres complexes. In Encyclopédie des sciences mathématiques, I 5, pages 329–468. Jacques Gabay, Paris, 1908. Élie Cartan. La topologie des espaces représentatifs groupes de Lie. L’Enseignement mathématique, 35:177–200, 1936. Élie Cartan. Leçons sur la Théorie des Spineurs. Hermann, Paris, 1938. Roger Carter, Graeme Segal, and Ian Macdonald. Lectures on Lie Groups and Lie Algebras. Cambridge University Press, Cambridge, 1995. Claude Chevalley. Theory of Lie Groups. I. Princeton Mathematical Series, vol. 8. Princeton University Press, Princeton, N. J., 1946. John H. Conway and Derek A. Smith. On Quaternions and Octonions. A K Peters Ltd., Natick, MA, 2003. 204
Bibliography 205 H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch, A. Prestel, and R. Remmert. Numbers. Springer-Verlag, New York, 1990. With an introduction by K. Lamotke, Translated from the second German edition by H. L. S. Orde, Translation edited and with a preface by J. H. Ewing. M. Eichler. A new proof of the Baker–Campbell–Hausdorff formula. Journal of the Mathematical Society of Japan, 20:23–25, 1968. Roger Godement. Introduction àlathéorie des groupes de Lie. Springer- Verlag, Berlin, 2004. Reprint of the 1982 original. Brian C. Hall. Lie Groups, Lie Algebras, and Representations. Springer- Verlag, New York, 2003. Sir William Rowan Hamilton. Researches respecting quaternions. In The Mathematical Papers of Sir William Rowan Hamilton, Vol. III, pages 159–226. Cambridge University Press, Cambridge, 1967. Thomas Hawkins. Emergence of the Theory of Lie Groups. Springer- Verlag, New York, 2000. David Hilbert. Foundations of Geometry. Translated from the tenth German edition by Leo Unger. First edition, 1899. Open Court, LaSalle, Ill., 1971. Roger Howe. Very basic Lie theory. Amer. Math. Monthly, 90(9):600–623, 1983. Camille Jordan. Mémoire sur les groupes de mouvements. Annali di matematiche, 2:167–215, 322–345, 1869. Irving Kaplansky. Lie algebras. In Lectures on Modern Mathematics, Vol. I, pages 115–132. Wiley, New York, 1963. L. Pontrjagin. Topological Groups. Princeton University Press, Princeton, 1939. Mark Ronan. Symmetry and the Monster. Oxford University Press, Oxford, 2006. Wulf Rossmann. Lie Groups. Oxford University Press, Oxford, 2002.
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:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
10 1 The geometry of complex number
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
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 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
show all

John Stillwell - Naive Lie Theory.pdf - Index of

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?