A survey of Lie groups and Lie algebras with applications and computational methods / Johan G.F. Belinfante, Bernard Kolman.
Series Classics in applied mathematics ; 2Editor: Philadelphia : Society for Industrial and Applied Mathematics, [1989], c1972Descripción: x, 164 p. : ill. ; 23 cmISBN: 0898712432 :Tema(s): Lie groups | Lie algebrasOtra clasificación: 22E70Introduction [3] Chapter 1 Lie Groups and Lie Algebras [5] 1.1 The general linear group [5] 1.2 Orthogonal and unitary groups [6] 1.3 Groups in geometry [7] 1.4 The exponential mapping [11] 1.5 Lie and associative algebras [12] 1.6 Lie groups [13] 1.7 Lie algebras of Lie groups [15] 1.8 Vector fields [18] 1.9 Lie theory of one-parameter groups [19] 1.10 Matrix Lie groups [21] 1.11 Poisson brackets [24] 1.12 Quantum symmetries [26] 1.13 Harmonic oscillators [30] 1.14 Lie subgroups and analytic homomorphisms [31] 1.15 Connected Lie groups [32] 1.16 Abelian Lie groups [34] 1.17 Low-dimensional Lie groups [35] 1.18 The covering group of the rotation group [36] 1.19 Tensor product of vector spaces [38] 1.20 Direct sums of vector spaces [42] 1.21 The lattice of ideals of a Lie algebra [43] 1.22 The Levi decomposition of a Lie algebra [44] 1.23 Semisimple Lie algebras [45] 1.24 The Baker-Campbell-Hausdorff formula [47] Chapter 2 Representation Theory [51] 2.1 Lie group representations [51] 2.2 Modules over Lie algebras [53] 2.3 Direct sum decompositions of Lie modules [56] 2.4 Lie module tensor product [57] 2.5 Tensor and exterior algebras [59] 2.6 The universal enveloping algebra of a Lie algebra [63] 2.7 Nilpotent and Cartan subalgebras [65] 2.8 Weight submodules [66] 2.9 Roots of semisimple Lie algebras [67] 2.10 The factorization method and special functions [70] 2.11The Cartan matrix [73] 2.12The Weyl group [74] 2.13Dynkin diagrams [76] 2.14Identification of simple Lie algebras [78] 2.15Construction of the Lie algebra A2 [79] 2.16Complexification and real forms [80] 2.17Real forms of the Lie algebra Ax [83] 2.18Angular momentum theory [86] Chapter 3 Constructive Methods [91] 3.1 32Raising and lowering subalgebras 91 Dynkin indices [93] 3.3Irreducible representations of Ax [95] 3.4The Casimir subalgebra [97] 3.5Irreducible representations of A2 [99] 3.6Characters [101] 3.7Computation of the Killing form [103] 3.8 Dynkin’s algorithm for the weight system [106] 3.9 Freudenthals algorithm [109] 3.10 The Weyl character formula [111] 3.11 The Weyl dimension formula [114] 3.12 Characters of modules over the algebra A2 [116] 3.13 The Kostant and Racah character formulas [117] 3.14 The Steinberg and Racah formulas for Clebsch-Gordan series [119] 3.15 Tensor analysis [122] 3.16 Young tableaux [124] 3.17 Contractions [128] 3.18 Spinor analysis and Clifford algebras [131] 3.19 Tensor operators [137] 3.20 Charge algebras [141] 321 Clebsch-Gordan coefficients [145] Bibliography [149] Index [159]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 22 B431 (Browse shelf) | Available | A-9309 |
Includes bibliographical references (p. 149-158).
Introduction [3]
Chapter 1 Lie Groups and Lie Algebras [5]
1.1 The general linear group [5]
1.2 Orthogonal and unitary groups [6]
1.3 Groups in geometry [7]
1.4 The exponential mapping [11]
1.5 Lie and associative algebras [12]
1.6 Lie groups [13]
1.7 Lie algebras of Lie groups [15]
1.8 Vector fields [18]
1.9 Lie theory of one-parameter groups [19]
1.10 Matrix Lie groups [21]
1.11 Poisson brackets [24]
1.12 Quantum symmetries [26]
1.13 Harmonic oscillators [30]
1.14 Lie subgroups and analytic homomorphisms [31]
1.15 Connected Lie groups [32]
1.16 Abelian Lie groups [34]
1.17 Low-dimensional Lie groups [35]
1.18 The covering group of the rotation group [36]
1.19 Tensor product of vector spaces [38]
1.20 Direct sums of vector spaces [42]
1.21 The lattice of ideals of a Lie algebra [43]
1.22 The Levi decomposition of a Lie algebra [44]
1.23 Semisimple Lie algebras [45]
1.24 The Baker-Campbell-Hausdorff formula [47]
Chapter 2 Representation Theory [51]
2.1 Lie group representations [51]
2.2 Modules over Lie algebras [53]
2.3 Direct sum decompositions of Lie modules [56]
2.4 Lie module tensor product [57]
2.5 Tensor and exterior algebras [59]
2.6 The universal enveloping algebra of a Lie algebra [63]
2.7 Nilpotent and Cartan subalgebras [65]
2.8 Weight submodules [66]
2.9 Roots of semisimple Lie algebras [67]
2.10 The factorization method and special functions [70]
2.11The Cartan matrix [73]
2.12The Weyl group [74]
2.13Dynkin diagrams [76]
2.14Identification of simple Lie algebras [78]
2.15Construction of the Lie algebra A2 [79]
2.16Complexification and real forms [80]
2.17Real forms of the Lie algebra Ax [83]
2.18Angular momentum theory [86]
Chapter 3 Constructive Methods [91]
3.1 32Raising and lowering subalgebras 91 Dynkin indices [93]
3.3Irreducible representations of Ax [95]
3.4The Casimir subalgebra [97]
3.5Irreducible representations of A2 [99]
3.6Characters [101]
3.7Computation of the Killing form [103]
3.8 Dynkin’s algorithm for the weight system [106]
3.9 Freudenthals algorithm [109]
3.10 The Weyl character formula [111]
3.11 The Weyl dimension formula [114]
3.12 Characters of modules over the algebra A2 [116]
3.13 The Kostant and Racah character formulas [117]
3.14 The Steinberg and Racah formulas for Clebsch-Gordan series [119]
3.15 Tensor analysis [122]
3.16 Young tableaux [124]
3.17 Contractions [128]
3.18 Spinor analysis and Clifford algebras [131]
3.19 Tensor operators [137]
3.20 Charge algebras [141]
321 Clebsch-Gordan coefficients [145]
Bibliography [149]
Index [159]
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