On representation-finite gendo-symmetric algebras with only one non-injective projective module
On representation-finite gendo-symmetric algebras with only one non-injective projective module
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DOI：
10.1016/j.jalgebra.2022.04.002
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发表时间：
2020-12
影响因子：
0.9
通讯作者：
T. Aihara;Aaron Chan;T. Honma
中科院分区：
文献类型：
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作者：
T. Aihara;Aaron Chan;T. Honma
受Schur代数和对称群的群代数之间的关系的启发，沿着代数李理论中的其他类似例子，Min Fang和Steffen Koenig [15]，[16]讨论了对称代数上生成元的自同态代数的一些行为，他们称之为根对称代数。继续这条工作线，我们在这篇文章中分类的表示有限的性别对称代数，只有一个同构类的不可分解的非内射投射模。我们还确定了它们的几乎ν-稳定的导出等价类在胡伟和席常昌[21]意义下的等价类.证明了一个表示有限对称代数的商可以通过某个不可分解投射模的基柱来选择一个表示。
Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig [15], [16] addressed some behaviour of the endomorphism algebra of a generator over a symmetric algebra, which they calledgendo-symmetric algebra. Continuing this line of works, we classify in this article the representation-finite gendo-symmetric algebras that have precisely one isomorphism class of indecomposable non-injective projective module. We also determine their almostν-stable derived equivalence classes in the sense of Wei Hu and Changchang Xi [21]. It turns out that a representative can be chosen as the quotient of a representation-finite symmetric algebra by the socle of a certain indecomposable projective module.