翻訳と辞書 Words near each other ・ Nicholls State Colonels women's basketball ・ Nicholls State University ・ Nicholls Town ・ Nicholls, Australian Capital Territory ・ Nicholls, Georgia ・ Nicholls-Crook House ・ Nichollsia ・ Nichollsia (disambiguation) ・ Nichollssaura ・ Nichollstown and Berry Islands ・ Nicholl–Lee–Nicholl ・ Nichols ・ Nichols (surname) ・ Nichols (TV series) ・ Nichols (village), New York ・ Nichols algebra ・ Nichols and May ・ Nichols and Shepard ・ Nichols Arboretum ・ Nichols Block ・ Nichols Bridgeway ・ Nichols Canyon, Los Angeles ・ Nichols cap guns ・ Nichols College ・ Nichols Farms Historic District ・ Nichols Field (Colorado) ・ Nichols Field (Philippines) ・ Nichols Hall ・ Nichols High School ・ Nichols Hills, Oklahoma 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 Nichols algebra ： ウィキペディア英語版 Nichols algebra In algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by $\backslash mathfrak(V)$ and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed Hopf algebra 〔 such as a quantum groups and their well known finite-dimensional truncations. Nichols algebras can immediately be used to write down new such quantum groups by using the Radford biproduct〔 The classification of all such Nichols algebras and even all associated quantum groups (see Application) is recently progressing rapidly, although still much is open: The case of an abelian group has been solved 2005,〔 but otherwise this phenomenon seems to be a very rare occasion, with a handful examples known and powerful negation criteria established (see below). Also, see here for a list List of finite-dimensional Nichols algebras. The finite-dimensional theory is greatly governed by a theory of root systems and Dynkin diagrams, strikingly similar to those of semisimple Lie algebras.〔 A comprehensive introduction is found in the lecture of Heckenberger 〔 ==Definition== Consider a Yetter–Drinfeld module ''V'' in the Yetter–Drinfeld category $^H\_H\backslash mathcal$ is always a Braided Hopf algebra. The coproduct $\backslash Delta$ and counit $\backslash epsilon$ of $TV$ is defined in such a way that the elements of $V$ are primitive, that is for all $v\backslash in\; V$ ::$\backslash Delta(v)=1\backslash otimes\; v+v\backslash otimes\; 1$ ::$\backslash epsilon(v)=0$ The Nichols algebra can be uniquely defined by several equivalent characterizations, some of which focus on the Hopf algebra structure and some are more combinatorial. Regardless, determining the Nichols algebra explicitly (even decide if it's finite-dimensional) can be very difficult and is open in several concrete instances (see below). 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「Nichols 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.