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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 Irreducible representation ： ウィキペディア英語版 Irreducible representation In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation $(\backslash Pi,\; V)$ or irrep of an algebraic structure $A$ is a nonzero representation that has no proper subrepresentation $(\backslash Pi,W),\; W\; \backslash subset\; V$ closed under the action of $\backslash Pi(a),\; a\backslash in\; A$. Every finite-dimensional unitary representation on a Hermitian vector space $V$ is the direct sum of irreducible representations. As irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), these terms are often confused; however, in general there are many reducible but indecomposable representations, such as the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices. ==History== Group representation theory was generalized by Richard Brauer from the 1940s to give modular representation theory, in which the matrix operators act over a field $K$ of arbitrary characteristic, rather than a vector of real or complex numbers. The structure analogous to an irreducible representation in the resulting theory is a simple module. 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「Irreducible representation」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.