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In mathematics, the nil-Coxeter algebra, introduced by , is an algebra similar to the group algebra of a Coxeter group except that the generators are nilpotent. ==Definition== The nil-Coxeter algebra for the infinite symmetric group is the algebra generated by ''u''1, ''u''2, ''u''3, ... with the relations *''u'' = 0 *''u''''i''''u''''j'' = ''u''''j''''u''''i'' if |''i'' − ''j''| > 1 *''u''''i''''u''''j''''u''''i'' = ''u''''j''''u''''i''''u''''j'' if |''i'' − ''j''| = 1 These are just the relations for the infinite braid group, together with the relations ''u'' = 0. Similarly one can define a nil-Coxeter algebra for any Coxeter system, by adding the relations ''u'' = 0 to the relations of the corresponding generalized braid 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「Nil-Coxeter algebra」の詳細全文を読む スポンサード リンク
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