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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 Rota–Baxter algebra ： ウィキペディア英語版 Rota–Baxter algebra In mathematics, a Rota–Baxter algebra is an algebra, usually over a field ''k'', together with a particular ''k''-linear map ''R'' which satisfies the weight-θ Rota–Baxter identity. It appeared first in the work of the American mathematician Glen E. Baxter in the realm of probability theory. Baxter's work was further explored from different angles by Gian-Carlo Rota,〔; ibid. 75, 330–334, (1969). Reprinted in: ''Gian-Carlo Rota on Combinatorics: Introductory papers and commentaries'', J.P.S. Kung Ed., Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1995.〕〔G.-C. Rota, ''Baxter operators, an introduction'', In: ''Gian-Carlo Rota on Combinatorics, Introductory papers and commentaries'', J.P.S. Kung Ed., Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1995.〕〔G.-C. Rota and D. Smith, ''Fluctuation theory and Baxter algebras'', Instituto Nazionale di Alta Matematica, IX, 179–201, (1972). Reprinted in: ''Gian-Carlo Rota on Combinatorics: Introductory papers and commentaries'', J.P.S. Kung Ed., Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1995.〕 Pierre Cartier, and Frederic V. Atkinson, among others. Baxter’s derivation of this identity that later bore his name emanated from some of the fundamental results of the famous probabilist Frank Spitzer in random walk theory. ==Definition and first properties== Let ''A'' be a ''k''-algebra with a ''k''-linear map ''R'' on ''A'' and let θ be a fixed parameter in ''k''. We call ''A'' a Rota-Baxter ''k''-algebra and ''R'' a Rota-Baxter operator of weight θ if the operator ''R'' satisfies the following Rota–Baxter relation of weight θ: :$R(x)R(y)\; +\; \backslash theta\; R(xy)\; =\; R(R(x)y\; +\; xR(y)).\backslash ,$ The operator ''R'':= θ ''id'' − ''R'' also satisfies the Rota–Baxter relation of weight θ. 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「Rota–Baxter algebra」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.