Algebras sharing the same support τ-tilting poset with tree quiver algebras
Algebras sharing the same support τ-tilting poset with tree quiver algebras
复制标题
与树袋代数共享相同支持 τ-倾斜偏序集的代数
DOI：
10.1093/qmath/hay025
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Kase Ryoichi
中科院分区：
文献类型：
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作者：
Aihara Takuma;Kase Ryoichi
Happel和Unger从倾斜模的偏序集重构了遗传代数。受这个结果的启发，我们试图消除遗传的假设。然而，不幸的是，它在一般情况下会失败：例如，每个自内射代数都有仅由一个点组成的偏序集。因此，我们应该考虑对支撑τ-倾斜模偏序集的Happel-Unger结果的一个推广，它包含了倾斜模偏序集的Happel-Unger结果。本文重点研究了支撑τ-倾斜偏序集与树代数的支撑τ-倾斜偏序集重合的有限维代数，并给出了这类代数的充分刻画。
Happel and Unger reconstructed hereditary algebras from their posets of tilting modules. Inspired by this result, we try removing the assumption to be hereditary. However, it would unfortunately fail in general: for example, every self-injective algebra has the poset consisting of only one point. Therefore, we should consider a generalization of the Happel–Unger result for posets of supportτ-tilting modules, which contains those of tilting modules. In this paper, we spotlight finite dimensional algebras whose supportτ-tilting posets coincide with those of tree quiver algebras and give a full characterization of such algebras.