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In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups are Hausdorff spaces. ==Compact Lie groups== Lie groups form a very nice class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups include * the circle group T and the torus groups T''n'', * the orthogonal groups O(''n''), the special orthogonal group SO(''n'') and its covering spin group Spin(''n''), * the unitary group U(''n'') and the special unitary group SU(''n''), * the symplectic group Sp(''n''), * the compact forms of the exceptional Lie groups: G2, F4, E6, E7, and E8, The classification theorem of compact Lie groups states that up to finite extensions and finite covers this exhausts the list of examples (which already includes some redundancies). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「compact group」の詳細全文を読む スポンサード リンク
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