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Hochschild cohomology of truncated quiver algebras

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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 finite-dimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.

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Authors and Affiliations

  1. Faculty of Mathematics & Computer Science, Hubei University, Wuhan, 430062, China

    Yun-ge Xu & Wen-feng Jiang

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Yang Han

Authors
  1. Yun-ge Xu
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  2. Yang Han
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  3. Wen-feng Jiang
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Corresponding author

Correspondence to Yang Han.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10426014, 10501010 and 10201004), and Important Fund of Hubei Provincial Department of Education (Grant No. D200510005)

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Xu, Yg., Han, Y. & Jiang, Wf. Hochschild cohomology of truncated quiver algebras. SCI CHINA SER A 50, 727–736 (2007). https://doi.org/10.1007/s11425-007-2085-x

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  • DOI: https://doi.org/10.1007/s11425-007-2085-x

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