| Hochschild cohomology of truncated quiver algebras |
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| 引用本文： | Yun-ge XU,Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science,Hubei University,Wuhan 430062,China, Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China. Hochschild cohomology of truncated quiver algebras[J]. 中国科学A辑(英文版), 2007, 50(5): 727-736. DOI: 10.1007/s11425-007-2085-x |
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| 作者姓名： | Yun-ge XU Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science Hubei University Wuhan 430062 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China |
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| 作者单位： | Yun-ge XU，Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science，Hubei University，Wuhan 430062，China; Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.
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| 收稿时间： | 2005-09-10 |
| 修稿时间： | 2006-09-25 |
Hochschild cohomology of truncated quiver algebras |
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| Yun-ge Xu,Yang Han,Wen-feng Jiang. Hochschild cohomology of truncated quiver algebras[J]. Science in China(Mathematics), 2007, 50(5): 727-736. DOI: 10.1007/s11425-007-2085-x |
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| Authors: | Yun-ge Xu Yang Han Wen-feng Jiang |
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| Affiliation: | 1. Faculty of Mathematics & Computer Science, Hubei University, Wuhan 430062, China
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. |
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| Keywords: | truncated quiver algebra Hochschild cohomology global dimension oriented cycle |
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