循环单列代数的Hall代数

晋云 郭

doi:10.1360/za1994-24-2-139

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循环单列代数的Hall代数

晋云郭

Year: 1994 Journal: Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese) Vol: 24 (2)Pages: 139-149 Publisher: Science China Press

DOI: 10.1360/za1994-24-2-139

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Abstract

本文在(Z⁺)^nm上引入序<1和<2,通过(Z⁺)^nm与一个有n个单模且不可分解投射模长度为m的循环单列代数R的有限模同构类的一一对应,它们亦可视为后者的序. 由此我们证明了循环单列代数的Hall代数等同于它的Loewy子代数,它的有理扩张有一个BPW型的基,且是一个其相伴分次环为进代斜多项式环的((Z⁺)^nm,<2)滤环. 本文结论亦可推广到有限域上的管的Hall代数.

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循环单列代数的Hall代数

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