z阶顶点代数的Nakayama引理及其应用

IF 1.5 1区 数学 Q1 MATHEMATICS
Hao Wang , Wei Wang
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As an application, we investigate a specific triangulated Lie algebra: <span><math><mi>g</mi><mo>=</mo><mi>C</mi><mi>f</mi><mo>⊕</mo><mi>C</mi><mi>h</mi><mo>⊕</mo><mi>C</mi><mi>e</mi></math></span> with Lie brackets <span><math><mo>[</mo><mi>h</mi><mo>,</mo><mi>e</mi><mo>]</mo><mo>=</mo><mn>2</mn><mi>e</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>h</mi><mo>,</mo><mi>f</mi><mo>]</mo><mo>=</mo><mo>−</mo><mn>2</mn><mi>f</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>]</mo><mo>=</mo><mn>0</mn></math></span>. Denote the <span><math><mi>Z</mi></math></span>-graded vertex algebra constructed from <span><math><mi>g</mi></math></span> by <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>l</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. 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引用次数: 0

摘要

本文是一系列关于由三角形分解李代数产生的z梯度顶点代数的研究中的第一篇论文(为简单起见,称为三角化李代数)。本文建立了z阶顶点代数的Jacobson根理论,并证明了Nakayama引理。作为应用,我们研究了一类特殊的三角李代数:g=Cf⊕Ch⊕Ce,其中李括号[h,e]=2e,[h,f]= - 2f,[e,f]=0。表示由g由Vg(1,0)构造的z阶顶点代数。利用中山引理,对所有不可约容许的Vg(1,0)-模进行了分类。最后构造了一类不可分解可容许的Vg(1,0)-模。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nakayama's lemma for Z-graded vertex algebras and its applications
This is the first paper in a series of studies on Z-graded vertex algebras arising from Lie algebras with triangular decomposition (referred to as triangulated Lie algebras for simplicity). In this paper, we establish the Jacobson radical theory for Z-graded vertex algebras and prove Nakayama's lemma. As an application, we investigate a specific triangulated Lie algebra: g=CfChCe with Lie brackets [h,e]=2e,[h,f]=2f,[e,f]=0. Denote the Z-graded vertex algebra constructed from g by Vg(l,0). Using Nakayama's lemma, we classify all the irreducible admissible Vg(l,0)-modules. Finally, we construct a class of indecomposable admissible Vg(l,0)-modules.
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来源期刊
Advances in Mathematics
Advances in Mathematics 数学-数学
CiteScore
2.80
自引率
5.90%
发文量
497
审稿时长
7.5 months
期刊介绍: Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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