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In mathematics, a loop group is a group of loops in a topological group ''G'' with multiplication defined pointwise. ==Definition== In its most general form a loop group is a group of mappings from a manifold to a topological group . More specifically, let , the circle in the complex plane, and let denote the space of continuous maps , i.e. : equipped with the compact-open topology. An element of is called a ''loop'' in . Pointwise multiplication of such loops gives the structure of a topological group. Parametrize with , : and define multiplication in by : Associativity follows from associativity in . The inverse is given by : and the identity by : The space is called the free loop group on . A loop group is any subgroup of the free loop group . 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「loop group」の詳細全文を読む スポンサード リンク
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