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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 noncommutative torus ： ウィキペディア英語版 noncommutative torus In mathematics, and more specifically in the theory of C *-algebras, the noncommutative tori ''A''θ (also known as irrational rotation algebras when θ is irrational) are a family of noncommutative C *-algebras which generalize the algebra of continuous functions on the 2-torus. Many topological and geometric properties of the classical 2-torus have algebraic analogues for the noncommutative tori, and as such they are fundamental examples of a noncommutative space in the sense of Alain Connes. == Definition == For any irrational number ''θ'', the noncommutative torus ''A''''θ'' is the C *-subalgebra of $B(L^2(\backslash mathbb))$, the algebra of bounded linear operators of square-integrable functions on the unit circle of $\backslash mathbb$ generated by unitary elements $U$ and $V$, where $U(f)(z)=zf(z)$ and $V(f)(z)=f(e^z)$. A quick calculation shows that $VU\; =\; e^UV$.〔 〕 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「noncommutative torus」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.