| Tubular algebras and affine Kac-Moody algebras |
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| 引用本文： | Zheng-xin CHEN & Ya-nan LIN School of Mathematics and Computer Science,Pujian Normal University,Fuzhou 350007,China, School of Mathematical Sciences,Xiamen University,Xiamen 361005,China. Tubular algebras and affine Kac-Moody algebras[J]. 中国科学A辑(英文版), 2007, 50(4): 521-532. DOI: 10.1007/s11425-007-0020-9 |
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| 作者姓名： | Zheng-xin CHEN & Ya-nan LIN School of Mathematics and Computer Science Pujian Normal University Fuzhou 350007 China School of Mathematical Sciences Xiamen University Xiamen 361005 China |
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| 作者单位： | Zheng-xin CHEN & Ya-nan LIN School of Mathematics and Computer Science，Pujian Normal University，Fuzhou 350007，China; School of Mathematical Sciences，Xiamen University，Xiamen 361005，China |
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| 摘 要： | The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.
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| 收稿时间： | 2005-02-23 |
| 修稿时间： | 2006-10-18 |
Tubular algebras and affine Kac-Moody algebras |
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| Zheng-xin Chen,Ya-nan Lin. Tubular algebras and affine Kac-Moody algebras[J]. Science in China(Mathematics), 2007, 50(4): 521-532. DOI: 10.1007/s11425-007-0020-9 |
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| Authors: | Zheng-xin Chen Ya-nan Lin |
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| Affiliation: | 1. School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China
2. School of Mathematical Sciences,Xiamen University,Xiamen 361005,China |
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| Abstract: | The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules. |
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| Keywords: | tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root |
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