| Characteristic modules and tensor products over quasi-hereditary algebras |
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| 作者姓名： | Yue-hui ZHANG~ |
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| 作者单位： | Yue-hui ZHANG（Institute of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China） ;
Shi-ying SHEN（Department of Mathematics, Lishui University, Lishui 323000, China） ;
Ping-kai YE（Department of Mathematics, Lishui University, Lishui 323000, China） ; |
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| 摘 要： | 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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| 收稿时间： | 13 January 2006 |
| 修稿时间： | 12 September 2006 |
Characteristic modules and tensor products over quasi-hereditary algebras |
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| Yue-hui ZHANG.Characteristic modules and tensor products over quasi-hereditary algebras[J].Science in China(Mathematics),2007,50(8):1129-1140. |
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| Authors: | Yue-hui Zhang Shi-ying Shen Ping-kai Ye |
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| Institution: | 1. Institute of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China
2. Department of Mathematics, Lishui University, Lishui 323000, China |
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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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| Keywords: | quasi-hereditary algebra monomial algebra exact Borel subalgebra good module characteristic module |
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