Example image of eyePlorer eyePlorer map for 'Symplectic group': Group (mathematics) Mathematics Matrix (mathematics) Simple Lie group Élie Cartan Hermann Weyl Matrix multiplication Symplectic matrix Determinant Special linear group Subgroup Antisymmetric Bilinear form Degenerate form Linear map Vector space Symplectic vector space If and only if Complex number Lie group Real number Compact space Connected space Fundamental group Integer Lie algebra Simply connected space Transpose Quaternion Sesquilinear form Unitary group 3-sphere Special unitary group Conjugate transpose Skew-Hermitian matrix Complexification Killing form Metric signature Normal form Isomorphism Symplectic manifold Symplectic representation Hyperkähler manifold Jacobi form Metaplectic group Binary icosahedral group Binary octahedral group Binary tetrahedral group Segal-Shale-Weil distribution Bott periodicity theorem