Skew group algebras of Jacobian algebras
Skew group algebras of Jacobian algebras
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雅可比代数的斜群代数
DOI：
10.1016/j.jalgebra.2019.02.005
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发表时间：
2018
影响因子：
0.9
通讯作者：
A. Pasquali
中科院分区：
文献类型：
--
作者：
S. Giovannini;A. Pasquali
对于有限循环群G作用的位势箭图，我们研究了Jacobian代数Λ=P(Q，W)的斜群代数ΛG。通过Reiten和Riedtmann的结果，我们知道了一个基本代数η(ΛG)ηMorita等价于ΛG的箭图Q G。在一些关于G作用的假设下，我们显式地构造了QG上的位势WG，使得η(ΛG)η≅P(QG，WG)。如果Λ是自内射的，那么ΛG也是自内射的，我们研究了这种情况。受Herschend和Iyama刻画2-表示有限代数的启发，我们研究了(Q，W)上的割关于我们的构造的行为。
For a quiver with potential (Q, W) with an action of a finite cyclic group G, we study the skew group algebra ΛG of the Jacobian algebra Λ= P (Q, W). By a result of Reiten and Riedtmann, the quiver Q G of a basic algebra η (Λ G) η Morita equivalent to ΛG is known. Under some assumptions on the action of G, we explicitly construct a potential W G on Q G such that η (Λ G) η≅ P (Q G, W G). The original quiver with potential can then be recovered by the skew group algebra construction with a natural action of the dual group of G. If Λ is self-injective, then ΛG is as well, and we investigate this case. Motivated by Herschend and Iyama's characterisation of 2-representation finite algebras, we study how cuts on (Q, W) behave with respect to our construction.