Representation-finite trivial extension algebras
Representation-finite trivial extension algebras
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DOI：
10.1016/0022-4049(84)90058-6
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发表时间：
1984-09
影响因子：
0.8
通讯作者：
I. Assem;D. Happel;Óscar Roldán
中科院分区：
文献类型：
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作者：
I. Assem;D. Happel;Óscar Roldán
设A是代数闭域上的有限维基本连通结合代数，T（A）= A <$DA是它的极小内射余生成元的平凡扩张.证明了T（A）是Cartan类Δ的表示有限的当且仅当A是Dynkin类Δ的迭代倾斜代数.证明还产生了Dynkin型迭代倾斜代数的建设过程。
Let A be a finite-dimensional basic connected associative algebra over an algebraically closed field, and T (A)= A⋉ DA its trivial extension by its minimal injective cogenerator. We prove that T (A) is representation-finite of Cartan class Δ if and only if A is an iterated tilted algebra of Dynkin class Δ. The proof also yields a construction procedure for iterated tilted algebras of Dynkin type.