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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Additive K-theory ： ウィキペディア英語版 Additive K-theory In mathematics, additive K-theory means some version of algebraic K-theory in which, according to Spencer Bloch, the general linear group ''GL'' has everywhere been replaced by its Lie algebra ''gl''.〔http://www.math.uchicago.edu/~bloch/addchow_rept.pdf〕 It is not, therefore, one theory but a way of creating additive or infinitesimal analogues of multiplicative theories. ==Formulation== Following Boris Feigin and Boris Tsygan,〔B. Feigin, B. Tsygan. ''Additive K-theory'', LNM 1289, Springer〕 let $A$ be an algebra over a field $k$ of characteristic zero and let $(A)$ be the algebra of infinite matrices over $A$ with only finitely many nonzero entries. Then the Lie algebra homology :$H\_\backslash cdot\; ((A),k)\; \backslash ,$ has a natural structure of a Hopf algebra. The space of its primitive elements of degree $i$ is denoted by $K^+\_i(A)$ and called the $i$-th additive K-functor of ''A''. The additive K-functors are related to cyclic homology groups by the isomorphism :$HC\_i(A)\; \backslash cong\; K^+\_(A).\; \backslash ,$ 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「Additive K-theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.