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Characteristic modules and tensor products over quasi-hereditary algebras

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Abstract

Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B. It is proved that the category of induced good modules over B is contained in the category of good modules over A; that the characteristic module of A is an induced module of that of B via the exact functor — ⊗ B A if and only if the induced A-module of an injective B-module remains injective as a B-module. Moreover, it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.

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Authors and Affiliations

  1. Institute of Mathematics, Tianjin University of Technology and Education, Tianjin, 300222, China

    Yue-hui Zhang

  2. Department of Mathematics, Lishui University, Lishui, 323000, China

    Shi-ying Shen & Ping-kai Ye

Authors
  1. Yue-hui Zhang
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  2. Shi-ying Shen
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  3. Ping-kai Ye
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Correspondence to Yue-hui Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10601036)

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Zhang, Yh., Shen, Sy. & Ye, Pk. Characteristic modules and tensor products over quasi-hereditary algebras. SCI CHINA SER A 50, 1129–1140 (2007). https://doi.org/10.1007/s11425-007-0083-7

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  • DOI: https://doi.org/10.1007/s11425-007-0083-7

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