The Hall Algebra of Cyclic Serial Algebra  

作　　者：郭晋云 

机构地区：[1]Department of Mathematics, Hunan Normal University, Changsha 410081, PRC

出　　处：《Science China Mathematics》1994年第7期789-801,共13页中国科学：数学（英文版）

摘　　要：In this paper, orders <1 and <2 on ((Z)+)nm are introduced and also regarded as orders on the isomorphism classes of finite modules of finite .cyclic algebra R with n simple modules and all the indecomposable projective modules have length m through a one-to-one correspondence between ((Z)+)nm and the isomorphism classes of finite R modules. Using this we prove that the Hall algebra of a cyclic serial algebra is identified with its Loewy subalgebra, and its rational extension has a basis of BPW type, and is a (((Z)+)nm, <2) filtered ring with the associated graded ring as an iterated skew polynomial ring. These results are also generalized to the Hall algebra of a tube over a finite field.In this paper, orders &lt;1 and &lt;2 on ((Z)+)nm are introduced and also regarded as orders on the isomorphism classes of finite modules of finite .cyclic algebra R with n simple modules and all the indecomposable projective modules have length m through a one-to-one correspondence between ((Z)+)nm and the isomorphism classes of finite R modules. Using this we prove that the Hall algebra of a cyclic serial algebra is identified with its Loewy subalgebra, and its rational extension has a basis of BPW type, and is a (((Z)+)nm, &lt;2) filtered ring with the associated graded ring as an iterated skew polynomial ring. These results are also generalized to the Hall algebra of a tube over a finite field.

关 键 词：Hall ALGEBRA CYCLIC SERIAL ALGEBRA filtered RING ITERATED SKEW polynomial ring. 

分 类 号：O153[理学—数学]