翻訳と辞書 Words near each other ・ Quadrat (disambiguation) ・ Quadrat (hieroglyph block) ・ Quadratala ・ Quadratapora ・ Quadrate ・ Quadrate (heraldry) ・ Quadrate bone ・ Quadrate ligament ・ Quadrate line ・ Quadrate lobe of liver ・ Quadrate pebblesnail ・ Quadrate tubercle ・ Quadrathlon ・ Quadratic ・ Quadratic (collection) ・ Quadratic algebra ・ Quadratic assignment problem ・ Quadratic bottleneck assignment problem ・ Quadratic classifier ・ Quadratic configuration interaction ・ Quadratic differential ・ Quadratic eigenvalue problem ・ Quadratic equation ・ Quadratic field ・ Quadratic form ・ Quadratic form (statistics) ・ Quadratic formula ・ Quadratic Frobenius test ・ Quadratic function ・ Quadratic Gauss sum Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quadratic algebra ： ウィキペディア英語版 Quadratic algebra In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras. == Definition == A graded quadratic algebra ''A'' is determined by a vector space of generators ''V'' = ''A''1 and a subspace of homogeneous quadratic relations ''S'' ⊂ ''V'' ⊗ ''V'' . Thus : $A=T(V)/\backslash langle\; S\backslash rangle$ and inherits its grading from the tensor algebra ''T''(''V''). If the subspace of relations may also contain inhomogeneous degree 2 elements, ''S'' ⊂ ''k'' ⊕ ''V'' ⊕ (''V'' ⊗ ''V''), this construction results in a filtered quadratic algebra. A graded quadratic algebra ''A'' as above admits a quadratic dual: the quadratic algebra generated by ''V'' * and with quadratic relations forming the orthogonal complement of ''S'' in ''V'' * ⊗ ''V'' *. 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「Quadratic 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.