## 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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algebra U(L analytic angular momentum antisymmetric associative algebra automorphism basic modules basic weights basis bilinear form called Cartan matrix Cartan subalgebra Casimir classical Clebsch–Gordan coefficients Clebsch–Gordan series Clifford algebra commutation relations compact complex Lie algebra complexification compute coordinates corresponding decomposition defined differential equations dimension dynamical variables Dynkin diagram Dynkin indices eigenvalue elements Euclidean space finite-dimensional functions GL(n Hamiltonian hence highest weight Hilbert space homomorphism ideals integer invariant irreducible module isomorphic Lie algebra A1 Lie modules Lie product linear group linear mapping linear operator Lorentz group manifold Math Mathematical method multiplication nilpotent nonsingular normal subgroup obtain particle permutation Phys positive roots problem quantum mechanics real form real Lie algebra rotation group semisimple Lie algebra simple Lie algebra simple roots spanned spinor structure submodule subspace symmetry symplectic tangent space tensor algebra tensor powers tensor product theory of Lie transformations vector fields vector space weight system Weyl group Weyl reflections zero