| 模代数的形变理论 |
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| 引用本文： | 何济位.模代数的形变理论[J].数学学报,2004,47(5):947-956. |
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| 作者姓名： | 何济位 |
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| 作者单位： | 浙江大学西溪校区数学系,杭州,310028;绍兴文理学院数学系,绍兴,312000 |
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| 摘 要： | 本文构作了与模代数HA相适应的“形变复形”CH*(H,A),并利用形变复形的上同调群来刻画模代数HA的形变,证明了HA的无穷小形变的等价类是与形变复形的2阶上同调群HH2(H,A)是一一对应的,且当HH2(H,A)=0时,模代数HA为刚性的.
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| 关 键 词： | 模代数 形变 无穷小形变 |
| 文章编号： | 0583-1431(2004)05-0947-10 |
A Theory of Deformations of Module Algebras |
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| Ji Wei HE.A Theory of Deformations of Module Algebras[J].Acta Mathematica Sinica,2004,47(5):947-956. |
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| Authors: | Ji Wei HE |
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| Affiliation: | Ji Wei HE
(Department of Mathematics, Zhejiang University Xixi Campus, Hangzhou 310028, P. R. China) (Department of Mathematics, Shaoxing College of Arts and Science, Shaoxing 312000, P. R. China) |
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| Abstract: | We provide a "deformation complex" CH*(H, A) associated to a given module algebra HA, and use the cohomology of CH*(H,A) to describe the infinitesimal deformation of HA. We show that there is an one-to-one correspondence between the equivalence classes of the infinitesimal deformations and HH2(H,A), and HA is rigid if the 2-cohomology of the deformaton complex HH2(H, A) = 0. |
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| Keywords: | Module algebra Deformation Infinitesimal deformation |
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