Domestic法式代数的Hall代数的极小生成元集

Minimal Generators of Hall Algebras of Domestic Canonical Algebras

设A为有限域k上domestic法式代数.得到A的Hall代数H(A)中不可分解A-模同构类能由维数向量更小的A-模同构类生成的充要条件,给出H(A)的极小生成元集.进一步给出一个递推算法将不可分解例外模写成任一组极小生成元的Hall积的R-线性组合.

Let A be a domestic canonical algebra over a finite field k. All indecomposable A-modules, which can be generated by A-modules with ＂smaller＂ dimension vector inside the Hall algebra H（A） of A, are classified; then systems of minimal homogeneous generators of H（A） are explicitly written out. Moreover, give an inductive algorithm for the representation of an indecomposable exceptional module as a R-linear combination of Hall multipication of any system of minimal generators.