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The connected closed Subgroups (up to an Isomorphism) of Complex Matrices that are closed under conjugate transpose and have a discrete finite center. Examples include Special Linear Groups, Symplectic Groups, and certain isometry groups of Quadratic Forms.
See also Lie Group
References
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43,
537-549, 1996.