Automorphisms of Repetitive Algebras
Automorphisms of Repetitive Algebras
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重复代数的自同构
DOI：
10.1006/jabr.2000.8418
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发表时间：
2000
影响因子：
0.9
通讯作者：
K. Yamagata
中科院分区：
文献类型：
--
作者：
Y. Ohnuki;Kaoru Takeda;K. Yamagata
设B是域K上有限维代数B的重代数，B-双模DB=1Hom(B，K)，ν是B的Nakayama自同构.我们确定了B的正自同构ϕ，使得轨道代数B/(ϕν)通过B-双模(DB)β同构于B的可分扩张代数B的自同构β，并刻划了具有B的正自同构ϕν的弱对称代数和形式B/(ϕ)的对称代数。作为应用，我们刻画了一类具有非周期广义标准Auslander-Reiten分量的弱对称代数。
Abstract Let B be the repetitive algebra of a finite dimensional algebra B over a field K by the B -bimodule DB = Hom( B , K ), and let ν be the Nakayama automorphism of B . We determine the positive automorphisms ϕ of B such that the orbit algebra B /(ϕν) is isomorphic to a splittable extension algebra of B by the B -bimodule ( DB ) β for an automorphism β of B , and we characterize weakly symmetric algebras and symmetric algebras of the form B /(ϕν) with a positive automorphism ϕ of B . As an application, we characterize some class of weakly symmetric algebras with non-periodic generalized standard Auslander–Reiten components.