A survey of Lie groups and Lie algebras with applications and computational methods / Johan G.F. Belinfante, Bernard Kolman.

Por: Belinfante, Johan G. FColaborador(es): Kolman, Bernard, 1932-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: *CODIGO*
Contenidos:
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]
    Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Status Date due Barcode
Libros Libros 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]

MR, REVIEW #

There are no comments on this title.

to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a biblioteca.antonio.monteiro@gmail.com

Powered by Koha