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Lie Groups, Lie Algebras, and Fibre Bundles
Lie Groups, Lie Algebras, and Fibre Bundles
foundations +17 more results +43 more equations +35 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) notation 14.1: not:lie-indices 14.1 notation definition 14.2: Lie group 14.2 Lie group definition 14.5: Universal enveloping algebra 14.5 Universal envelo… definition 14.8: Casimir element 14.8 Casimir element notation 14.9: Casimirs against structure constants 14.9 Casimirs against… definition 14.10: Killing form 14.10 Killing form definition 14.14: Invariant symmetric tensor 14.14 Invariant symmet… definition 14.20: Cartan subalgebra and rank 14.20 Cartan subalgebr… definition 14.26: The rotation group 14.26 The rotation gro… definition 14.28: Hermitian rotation generators 14.28 Hermitian rotati… definition 14.32: The special unitary group in two dimensions 14.32 The special unit… definition 14.40: Ladder operators and the Casimir 14.40 Ladder operators… definition 14.49: The special unitary group in three dimensions 14.49 The special unit… proposition 14.3: A one-parameter subgroup is an exponential 14.3 A one-parameter… theorem 14.7: Poincaré–Birkhoff–Witt 14.7 Poincaré–Birkhof… lemma 14.11: Invariance of the Killing form 14.11 Invariance of th… corollary 14.12: Total antisymmetry of the structure constants 14.12 Total antisymmet… theorem 14.13: Cartan's criterion 14.13 Cartan's criteri… theorem 14.16: Invariant tensors give Casimir operators 14.16 Invariant tensor… corollary 14.17: The quadratic Casimir 14.17 The quadratic Ca… corollary 14.18: A Casimir acts as a number on an irreducible
representation 14.18 A Casimir acts a… theorem 14.21: Racah 14.21 Racah proposition 14.22: The rank of so(p,q) 14.22 The rank of so(p… proposition 14.27: Generators of so(3) 14.27 Generators of so… proposition 14.30: Rodrigues formula; the exponential map is onto 14.30 Rodrigues formul… proposition 14.31: SO(3,ℝ) is not simply connected 14.31 SO(3,ℝ) is not s… equation 14.2: eq:lie-varincor eq. (14.2) equation 14.3: eq:lie-generators eq. (14.3) equation 14.4: eq:lie-gengrlie eq. (14.4) equation 14.5: eq:lie-structconst eq. (14.5) equation 14.6: eq:lie-expgen eq. (14.6) equation 14.10: eq:lie-genalt eq. (14.10) equation 14.12: eq:lie-uea-relations eq. (14.12) equation 14.15: eq:lie-killing-components eq. (14.15) equation 14.22: eq:lie-sopq-rank eq. (14.22) equation 14.23: eq:lie-sopq-defining eq. (14.23) equation 14.25: eq:lie-so2-matrix eq. (14.25) equation 14.28: eq:lie-expso2 eq. (14.28) equation 14.29: eq:lie-so2-irreps eq. (14.29) The chain of Lie Groups, Lie Algebras, and Fibre Bundles: 39 of 134 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.