| Hochschild （Co）homology of Galois Coverings of Grassmann Algebras |
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| 引用本文： | Yun Ge XU,Xin TANG. Hochschild （Co）homology of Galois Coverings of Grassmann Algebras[J]. 数学学报(英文版), 2009, 25(10): 1693-1702. DOI: 10.1007/s10114-009-7346-x |
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| 作者姓名： | Yun Ge XU Xin TANG |
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| 作者单位： | [1]School of Mathematics and Computer Science, Hubei University, Wuhan 430062, P.R. China [2]Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC 28301, USA |
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| 基金项目： | Supported by NationafNatrual Science Foundation of China （Grant No. 10501010） |
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| 摘 要： | Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.
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| 关 键 词： | 格拉斯曼代数 同源性 伽罗瓦 Hochschild 防蚀 CO 霍克 上同调群 |
Hochschild (co)homology of Galois coverings of Grassmann algebras |
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| Yun Ge Xu,Xin Tang. Hochschild (co)homology of Galois coverings of Grassmann algebras[J]. Acta Mathematica Sinica(English Series), 2009, 25(10): 1693-1702. DOI: 10.1007/s10114-009-7346-x |
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| Authors: | Yun Ge Xu Xin Tang |
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| Affiliation: | 1.School of Mathematics and Computer Science,Hubei University,Wuhan,P.R. China;2.Department of Mathematics and Computer Science,Fayetteville State University,Fayetteville,USA |
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| Abstract: | Let $
tilde Lambda
$
tilde Lambda
be the ℤ2-Galois covering of the Grassmann algebra Λ over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of $
tilde Lambda
$
tilde Lambda
are calculated explicitly. And the cyclic homology of $
tilde Lambda
$
tilde Lambda
can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from ⊕ i≥1 HH i ($
tilde Lambda
$
tilde Lambda
) to ⊕ i≥1 HH i (Λ). |
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| Keywords: | Galois covering Grassmann algebra Hochschild （co）homology minimal projective resolution |
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