Research Catalog

Title

A survey of Lie groups and Lie algebras with applications and computational methods [by] Johan G.F. Belinfante [and] Bernard Kolman.

Author

Belinfante, Johan G. F.

Publication

Philadelphia, Society for Industrial and Applied Mathematics [1972]

Items in the Library & Off-site

Details

Additional Authors

Kolman, Bernard, 1932-

Description

ix, 164 pages; 26 cm.

Series Statement

Classics in applied mathematics.

Uniform Title

Classics in applied mathematics

Subject

• Lie groups
• Lie algebras
• Lie algebras
• Lie groups
• Lie-Algebra
• Lie-Gruppe
• LIE GROUPS
• ALGEBRA

Bibliography (note)

• Bibliography: p. 149-158.

Contents

Lie group and lie algebras : The general linear group ; Orthogonal and unitary groups ; Groups in geometry ; The exponential mapping ; Lie and associative algebras ; Lie groups ; Lie algebras of lie groups ; Vector fields ; Lie theory of one parameter groups ; Matrix lie groups ; Poisson brackets ; Quantum symmetries ; Harmonic oscillators ; Lie subgroups and analytic homomorphisms ; Connected lie groups ; Abelian lie groups ; Low-dimensional lie groups ; The covering group of the rotation ; Tensor product of vector ; Direct sums of vector spaces ; The lattice of ideals of a lie algebra ; The Levi decomposition of a lie algebras ; Semi simple lie algebras ; The baker-Campbell-Harsdorf formula -- Representation theory : Lie group representations ; Modules of lie algebras ; Direct sum decompositions of lie modules ; Lie module tensor product ; Tensor and exterior algebras ; The universal enveloping algebra ; Nilpotent and Cartan subalgebras ; Weight submodules ; Roots of semi simple lie algebras ; The factorization method and special functions ; The Cartan matrix ; The Weyl group ; Dynkin diagrams ; Identification of simple lie algebras ; Construction of simple lie algebras ; Construction of the lie algebra A2 ; Complexification and real forms ; Real forms of the lie algebra A1 ; Angular momentum theory -- Raising and lowering subalgebras : Dynkin indices ; Irreducible representations of A1 ; The Casimir subalgebra ; Irreducible representations of A2 ; Characters ; Computation of the killing form ; Dynkin’s algorithm for the weight system ; Freudenthal’s algorithm ; The Weyl characters formula ; The Weyl dimension formula ; Characters of modules over the algebra A2 ; The Kostant and Racah character formulas ; The Steinberg and Racah formulas for Clebsch-Gordan series ; Tensor analysis ; Young tableaux ; Contractions ; Spinor analysis and Clifford algebras ; Tensor operators ; Charge algebras ; Clebsch-Gordan coefficients.

LCCN

72077081

OCLC

• ocm00520935
• 520935
• SCSB-255097

Owning Institutions

Princeton University Library