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The Characteristic Morphism of an Algebra

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Abstract

This paper is motivated by the observation that the characteristic morphism of an algebra relates to certain smoothness condition closely. We show that for an algebra A of finite global dimension, if the characteristic morphism is injective, then A has finite Hochschild cohomology dimension. In particular, if A is semi-simple, then the characteristic morphism is injective if and only if A is homologically smooth. Moreover, the characteristic morphism of a finite dimensional path algebra is injective. Recall that a path algebra is always homologically smooth.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Bing Wang & Yu Ye

  2. Department of Mathematics, The University of Texas, 1 University Station C1200, Austin, TX, 78712, USA

    Yuan Yao

  3. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, People’s Republic of China

    Yu Ye

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  1. Bing Wang
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  2. Yuan Yao
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  3. Yu Ye
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Correspondence to Yu Ye.

Additional information

Supported by the National Nature Science Foundation of China, grant no. 11431010 and no. 11571329.

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Wang, B., Yao, Y. & Ye, Y. The Characteristic Morphism of an Algebra. Appl Categor Struct 25, 971–990 (2017). https://doi.org/10.1007/s10485-016-9437-z

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