| $T_{2}(T)$的几乎可裂序列及几乎$mathcal {D}$-可裂序列 |
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| 引用本文： | 张玉林,姚海楼. $T_{2}(T)$的几乎可裂序列及几乎$mathcal {D}$-可裂序列[J]. 数学研究及应用, 2013, 33(1): 11-22 |
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| 作者姓名： | 张玉林 姚海楼 |
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| 作者单位： | 北京工业大学应用数理学院, 北京 100124;北京工业大学应用数理学院, 北京 100124 |
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| 基金项目： | 国家自然科学基金(Grant No.10971172); 北京市自然科学基金(Grant Nos.1092002; 1122002). |
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| 摘 要： | The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and D-split sequences. So in order to study the representations of triangular matrix algebra T2 (T ) = T0TT where T is a finite dimensional algebra over a field, it is important to determine its AR-sequences and D-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and D-split sequences of T2 (T) through the corresponding morphisms and sequences of T. Some interesting results are obtained.
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| 关 键 词： | algebras modules triangular matrix algebras AR sequences approximations. |
| 收稿时间： | 2011-07-15 |
| 修稿时间： | 2011-10-31 |
The Almost Split Sequences and ${cal D}$-Split Sequences of $T_{2}(T)$ |
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| Yulin ZHANG and Hailou YAO. The Almost Split Sequences and ${cal D}$-Split Sequences of $T_{2}(T)$[J]. Journal of Mathematical Research with Applications, 2013, 33(1): 11-22 |
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| Authors: | Yulin ZHANG and Hailou YAO |
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| Affiliation: | College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China;College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China |
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| Abstract: | The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and ${cal D}$-split sequences. So in order to study the representations of triangular matrix algebra $T_{2}(T)=begin{pmatrix} T & 0 T & T end{pmatrix}$ where $T$ is a finite dimensional algebra over a field, it is important to determine its AR-sequences and ${cal D}$-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and ${cal D}$-split sequences of $T_{2}(T)$ through the corresponding morphisms and sequences of $T$. Some interesting results are obtained. |
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| Keywords: | algebras modules triangular matrix algebras AR sequences approximations. |
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