Author | Hall, Brian C. author |
---|---|
Title | Lie Groups, Lie Algebras, and Representations [electronic resource] : An Elementary Introduction / by Brian C. Hall |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-0-387-21554-9 |
Descript | XIV, 354 p. online resource |
I General Theory -- 1 Matrix Lie Groups -- 2 Lie Algebras and the Exponential Mapping -- 3 The Baker-Campbell-Hausdorff Formula -- 4 Basic Representation Theory -- II Semisimple Theory -- 5 The Representations of SU(3) -- 6 Semisimple Lie Algebras -- 7 Representations of Complex Semisimple Lie Algebras -- 8 More on Roots and Weights -- A A Quick Introduction to Groups -- A.1 Definition of a Group and Basic Properties -- A.2 Examples of Groups -- A.2.1 The trivial group -- A.2.2 The integers -- A.2.4 Nonzero real numbers under multiplication -- A.2.5 Nonzero complex numbers under multiplication -- A.2.6 Complex numbers of absolute value 1 under multiplication -- A.2.7 The general linear groups -- A.2.8 Permutation group (symmetric group) -- A.3 Subgroups, the Center, and Direct Products -- A.4 Homomorphisms and Isomorphisms -- A.5 Quotient Groups -- A.6 Exercises -- B Linear Algebra Review -- B.1 Eigenvectors, Eigenvalues, and the Characteristic Polynomial -- B.2 Diagonalization -- B.3 Generalized Eigenvectors and the SN Decomposition -- B.4 The Jordan Canonical Form -- B.5 The Trace -- B.6 Inner Products -- B.7 Dual Spaces -- B.8 Simultaneous Diagonalization -- C More on Lie Groups -- C.1 Manifolds -- C.1.1 Definition -- C.1.2 Tangent space -- C.1.3 Differentials of smooth mappings -- C.1.4 Vector fields -- C.1.5 The flow along a vector field -- C.1.6 Submanifolds of vector spaces -- C.1.7 Complex manifolds -- C.2 Lie Groups -- C.2.1 Definition -- C.2.2 The Lie algebra -- C.2.3 The exponential mapping -- C.2.4 Homomorphisms -- C.2.5 Quotient groups and covering groups -- C.2.6 Matrix Lie groups as Lie groups -- C.2.7 Complex Lie groups -- C.3 Examples of Nonmatrix Lie Groups -- C.4 Differential Forms and Haar Measure -- D Clebsch-Gordan Theory for SU(2) and the Wigner-Eckart Theorem -- D.1 Tensor Products of sl(2; ?) Representations -- D.2 The Wigner-Eckart Theorem -- D.3 More on Vector Operators -- E Computing Fundamental Groups of Matrix Lie Groups -- E.1 The Fundamental Group -- E.2 The Universal Cover -- E.3 Fundamental Groups of Compact Lie Groups I -- E.4 Fundamental Groups of Compact Lie Groups II -- E.5 Fundamental Groups of Noncompact Lie Groups -- References