| Kac—Moody群的无限维代数子群 |
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| 引用本文： | 黄临文,查建国.Kac—Moody群的无限维代数子群[J].同济大学学报(自然科学版),1998,26(1):9-13. |
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| 作者姓名： | 黄临文 查建国 |
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| 作者单位： | 同济大学应用数学系!上海，200092 |
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| 基金项目： | 国家自然科学基金!19471059 |
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| 摘 要： | Ｓ．Ｐ．Ｗａｎｇ在文献中已经提出了Ｋａｃ－Ｍｏｏｄｙ群的有限维代数子群的概念。笔者首先把Ｃｈｅｖａｌｌｅｙ闭子群定理推广到Ｋａｃ－Ｍｏｏｄｙ群的有限维代数子群，即定理１．３。其次，通过子群和子代数之间的对应建立了Ｋａｃ－Ｍｏｏｄｙ群的无限维代数子群，并且证明无限维代数子群的说法是有限维代数子群的推广。
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| 关 键 词： | Kac－Moody群 Kac－Moody代数 无限维代数子群 |
Infinite-dimensional Algebraic Subgroups of Kac-Moody Groups |
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| Huang Linwen, Zha Jianguo.Infinite-dimensional Algebraic Subgroups of Kac-Moody Groups[J].Journal of Tongji University(Natural Science),1998,26(1):9-13. |
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| Authors: | Huang Linwen Zha Jianguo |
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| Abstract: | Prof. S. P. Wang has established the notion of finite -- dimensional algebraic subgroups of a Kac -- Moody group. In the paper, we first generalize Chevalley closed subgroups theorem to finite -- dimentional algebraic subgroups of Kac -- Moody groups. This is the content of theorem 1. 3. Second, we establish infinite -- dimensional algebraic subgroups of a Kac -- Moody group through the correspondence between subgroups and subalgebras, and verify that the notion of infinite -- dimensional algebraic subgroups is a generalization of the finite -- dimensional ones. |
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| Keywords: | Kac-Moody groups Kac-Moody algebras Algebraic groups |
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