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- Symplectic_group abstract "In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted Sp(2n, F) and Sp(n). The latter is sometimes called the compact symplectic group to distinguish it from the former. Many authors prefer slightly different notations, usually differing by factors of 2. The notation used here is consistent with the size of the matrices used to represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn, and Sp(n) is the compact real form of Sp(2n, C). Note that when we refer to the (compact) symplectic group it is implied that we are talking about the collection of (compact) symplectic groups, indexed by their dimension n.The name "symplectic group" is due to Hermann Weyl (details) as a replacement for the previous confusing names of (line) complex group and Abelian linear group, and is the Greek analog of "complex".".
- Symplectic_group wikiPageExternalLink 0503237.
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- Symplectic_group wikiPageRevisionID "677681938".
- Symplectic_group wikiPageWikiLink 3-sphere.
- Symplectic_group wikiPageWikiLink Addison-Wesley.
- Symplectic_group wikiPageWikiLink Addison-Wesley_Publishing_Company.
- Symplectic_group wikiPageWikiLink ArXiv.
- Symplectic_group wikiPageWikiLink Bilinear_form.
- Symplectic_group wikiPageWikiLink Canonical_commutation_relation.
- Symplectic_group wikiPageWikiLink Canonical_coordinates.
- Symplectic_group wikiPageWikiLink Canonical_transformation.
- Symplectic_group wikiPageWikiLink Canonical_transformations.
- Symplectic_group wikiPageWikiLink Category:Lie_groups.
- Symplectic_group wikiPageWikiLink Category:Symplectic_geometry.
- Symplectic_group wikiPageWikiLink Center_(group_theory).
- Symplectic_group wikiPageWikiLink Centre_(group_theory).
- Symplectic_group wikiPageWikiLink Characteristic_(algebra).
- Symplectic_group wikiPageWikiLink Classical_group.
- Symplectic_group wikiPageWikiLink Compact_group.
- Symplectic_group wikiPageWikiLink Compact_space.
- Symplectic_group wikiPageWikiLink Complex_number.
- Symplectic_group wikiPageWikiLink Complexification.
- Symplectic_group wikiPageWikiLink Conjugate_transpose.
- Symplectic_group wikiPageWikiLink Connected_space.
- Symplectic_group wikiPageWikiLink Degenerate_bilinear_form.
- Symplectic_group wikiPageWikiLink Determinant.
- Symplectic_group wikiPageWikiLink Diagonal_matrix.
- Symplectic_group wikiPageWikiLink Diffeomorphism.
- Symplectic_group wikiPageWikiLink Exponential_map_(Lie_theory).
- Symplectic_group wikiPageWikiLink Field_(mathematics).
- Symplectic_group wikiPageWikiLink Fundamental_group.
- Symplectic_group wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Symplectic_group wikiPageWikiLink Group_(math).
- Symplectic_group wikiPageWikiLink Group_(mathematics).
- Symplectic_group wikiPageWikiLink Group_action.
- Symplectic_group wikiPageWikiLink Group_isomorphism.
- Symplectic_group wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Symplectic_group wikiPageWikiLink Hamiltonian_matrix.
- Symplectic_group wikiPageWikiLink Hamiltonian_mechanics.
- Symplectic_group wikiPageWikiLink Heisenberg_picture.
- Symplectic_group wikiPageWikiLink Hermann_Weyl.
- Symplectic_group wikiPageWikiLink Hermitian_form.
- Symplectic_group wikiPageWikiLink Hilbert_space.
- Symplectic_group wikiPageWikiLink If_and_only_if.
- Symplectic_group wikiPageWikiLink Integer.
- Symplectic_group wikiPageWikiLink Integers.
- Symplectic_group wikiPageWikiLink Isomorphic.
- Symplectic_group wikiPageWikiLink Isomorphism.
- Symplectic_group wikiPageWikiLink Lie_algebra.
- Symplectic_group wikiPageWikiLink Lie_algebras.
- Symplectic_group wikiPageWikiLink Lie_group.
- Symplectic_group wikiPageWikiLink Linear_map.
- Symplectic_group wikiPageWikiLink Linear_transformations.
- Symplectic_group wikiPageWikiLink Manifold.
- Symplectic_group wikiPageWikiLink Mathematics.
- Symplectic_group wikiPageWikiLink Matrix_(math).
- Symplectic_group wikiPageWikiLink Matrix_(mathematics).
- Symplectic_group wikiPageWikiLink Matrix_multiplication.
- Symplectic_group wikiPageWikiLink Metaplectic_group.
- Symplectic_group wikiPageWikiLink Metric_signature.
- Symplectic_group wikiPageWikiLink Nondegenerate_form.
- Symplectic_group wikiPageWikiLink Orthogonal_group.
- Symplectic_group wikiPageWikiLink Phase_space.
- Symplectic_group wikiPageWikiLink Positive-definite_matrix.
- Symplectic_group wikiPageWikiLink Projective_unitary_group.
- Symplectic_group wikiPageWikiLink Quantum_state.
- Symplectic_group wikiPageWikiLink Quaternion.
- Symplectic_group wikiPageWikiLink Real_form.
- Symplectic_group wikiPageWikiLink Real_form_(Lie_theory).
- Symplectic_group wikiPageWikiLink Real_number.
- Symplectic_group wikiPageWikiLink SU(2).
- Symplectic_group wikiPageWikiLink Semisimple_Lie_algebra.
- Symplectic_group wikiPageWikiLink Sesquilinear_form.
- Symplectic_group wikiPageWikiLink Simple_Lie_algebra.
- Symplectic_group wikiPageWikiLink Simple_Lie_group.
- Symplectic_group wikiPageWikiLink Simply_connected.
- Symplectic_group wikiPageWikiLink Simply_connected_space.
- Symplectic_group wikiPageWikiLink Skew-Hermitian.
- Symplectic_group wikiPageWikiLink Skew-symmetric_matrix.
- Symplectic_group wikiPageWikiLink Special_linear_group.
- Symplectic_group wikiPageWikiLink Special_unitary_group.
- Symplectic_group wikiPageWikiLink Split_Lie_algebra.
- Symplectic_group wikiPageWikiLink Springer-Verlag.
- Symplectic_group wikiPageWikiLink Springer_Science+Business_Media.
- Symplectic_group wikiPageWikiLink Subgroup.
- Symplectic_group wikiPageWikiLink Surjective_function.
- Symplectic_group wikiPageWikiLink Symmetric_matrix.
- Symplectic_group wikiPageWikiLink Symplectic_geometry.
- Symplectic_group wikiPageWikiLink Symplectic_manifold.
- Symplectic_group wikiPageWikiLink Symplectic_matrix.
- Symplectic_group wikiPageWikiLink Symplectic_representation.
- Symplectic_group wikiPageWikiLink Symplectic_topology.
- Symplectic_group wikiPageWikiLink Symplectic_vector_space.
- Symplectic_group wikiPageWikiLink Symplectomorphism.
- Symplectic_group wikiPageWikiLink Tangent_space.
- Symplectic_group wikiPageWikiLink Transpose.
- Symplectic_group wikiPageWikiLink Unitary_group.