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Orthogonal groupSpecial linear groupSpecial linear lie algebraGeneral linear groupAffine groupLinear algebraic groupAdjoint representationSpecial unitary groupEuclidean groupIsometry groupLie algebraAutomorphism groupModular groupOrthonormal basisSelberg trace formulaGrassmannianBilinear formLie's third theoremComposition algebraSpin representationDifferential invariantFundamental representationSymmetric spaceSymmetric groupOrthogonal functionsSymmetry groupSymmetric bilinear formLie algebra representationHodge star operatorLattice of subgroupsProjective linear groupRepresentation of a lie groupRegular representationCartan decompositionInvertible matrixOrthogonal basisOrthogonal transformationOrthogonal matrixGroup representationSymplectic manifoldOrthogonalityMatrix pencilLatticeTensor productNormal subgroupPermutation groupIsogenyComplex lie groupBraid groupEuclidean topologyLinear groupCircle groupInteger latticeDual spaceSymplectic vector spaceProjective unitary groupAlternating multilinear mapKleinian groupLinear mapAutomorphic formIsometryBilinear mapPolarizationArithmetic groupDerivative of the exponential mapAlgebraic groupOrthogonal diagonalizationAlgebraic torusDegenerate bilinear formDefinite quadratic formCongruence subgroupLinear differential equationGroupLie bracket of vector fieldsIdeal class groupMultilinear formLie groupGroup of lie typeRigid transformationCharacteristic polynomialFundamental groupSemisimple lie algebraQuadratic formCartan subalgebraPoisson manifold3d rotation groupSpectrumAlgebra over a fieldConformal groupEuclidean plane isometryIrreducible representationInvariants of tensorsGroup actionMapping class groupSymmetric algebraAffine spaceSelf-adjoint operatorProjective representationReal coordinate spaceOrthogonal polynomials