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reductive group

约化群

本站译名 表示论与李理论 义项编号TS-1322

英文别名
reductive algebraic group
中文别名
简约代数群;约化代数群

外文出处

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Introduction to Mathematical Logic, Sixth Edition 封面

《Introduction to Mathematical Logic, Sixth Edition》 · 印刷第 35 页 Section 1.4 的底域约定,以及第 163 页 Section 3.3.1「Reductive Groups」标题、完全可约条件和 Definition 3.3.1;此教材采用复域情形,不要求群连通

The final structural result that we need for Chapter 12 is the Gauss decomposition of $G$ relative to a diagonal torus $A \subset G$ (the factorization of a matrix as a product of a block upper-triangular unipotent matrix, a block-diagonal matrix, and a block lower-triangular unipotent matrix, with the block sizes determined by the multiplicities of the weights of $A$).

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