Research Catalog

Details

Additional authors

1. Kolman, Bernard, 1932-

Description

1. ix, 164 pages; 26 cm.

Series statement

1. Classics in applied mathematics.

Uniform title

1. Classics in applied mathematics

Subject

1. Lie groups
2. Lie algebras
3. Lie algebras
4. Lie groups
5. Lie-Algebra
6. Lie-Gruppe
7. LIE GROUPS
8. ALGEBRA

Contents

1. 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.

Owning institution

1. Princeton University Library

Bibliography (note)

1. Bibliography: p. 149-158.