A Survey of Lie Groups and Lie Algebras with Applications and Computational MethodsIn this reprint edition, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed |
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Common terms and phrases
A₂ analytic antisymmetric associative algebra basic modules basic weights basis bilinear form C+(M Cartan matrix Cartan subalgebra classical Clebsch-Gordan series Clifford algebra commutation relations complex Lie algebra complex numbers compute coordinates corresponding decomposition defined differential equations dimension direct sum dynamical variables Dynkin diagram e₁ eigenvalue elements Euclidean space finite-dimensional formula functions GL(n Hamiltonian hence highest weight Hilbert space homomorphism ideals identity integer invariant irreducible module isomorphic j₁ Lie algebra A₁ Lie modules Lie product linear group linear mapping linear operator Lorentz group M₁ M₂ manifold Math multiplication nilpotent nonsingular obtain particle permutation positive roots quantum mechanics real form real Lie algebra rotation group S₁ semisimple Lie algebra simple Lie algebra simple roots spanned spinor structure submodule subspace symmetry symplectic tangent space tensor algebra tensor powers tensor product unitary V₁ V₂ vector fields vector space weight system Weyl group x₁ zero αι λ₁