A11的合成代数的三角分解

数学物理学报 ›› 1998, Vol. 18 ›› Issue (1): 11-18.

A₁₁的合成代数的三角分解

张顺华

山东大学数学院济南 250100

收稿日期:1996-03-11 修回日期:1996-09-28 出版日期:1998-03-26 发布日期:1998-03-26

Triangular Decomposition of the Composition Algebra of A₁₁

Zhang Shunhua

Deparment of mathematics, Shandong University, Jinan 250100

Received:1996-03-11 Revised:1996-09-28 Online:1998-03-26 Published:1998-03-26

摘要/Abstract

摘要： 设A是有限域上的A₁₁型的遗传代数,H(A)和C(A)分别表示A的Ringel-Hall代数和合成代数.该文证明了C(A)=Y·J·g其中Y和g分别表示由预投射模和预内射模生成的子代数,J是由C(A)中的正则元素生成的子代数.

关键词: Ringel-Hall代数, 合成代数, 预投射模, 预内射模和正则模

Abstract: Let A be the hereditary algebra of type A₁₁ over a finite field, H(A) and C(A) be respectively the Ringel-Hell algebra ang the Composition algebre. It is proved C(A)=Y·J·g,where P(resp.g) is the subalgebra of C(A) generated by the preprojective (rcsp. preinjective) A -modules, and J is the subalgebra generated by the regular elements of C(A).

Key words: Ringel-Hall algebra, Composition algebra, Preprojective modules, Preinjectivemodules, Regular modules

张顺华. A₁₁的合成代数的三角分解[J]. 数学物理学报, 1998, 18(1): 11-18.

Zhang Shunhua. Triangular Decomposition of the Composition Algebra of A₁₁[J]. Acta mathematica scientia,Series A, 1998, 18(1): 11-18.

A₁₁的合成代数的三角分解

Triangular Decomposition of the Composition Algebra of A₁₁

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