论文标题
在$τ$上 - 在温和的树代数的微不足道扩展上使用模块
On $τ$-tilting modules over trivial extensions of gentle tree algebras
论文作者
论文摘要
我们表明，柔和的树代数的微不足道的扩展是毫无疑问的顶点的Brauer Tree代数。我们还为代数的表征为琐碎的延伸是Brauer Line/Star/Cycle代数。结果，柔和的树代代数$ a $的支持$τ$的支持$τ$的数量仅取决于简单$ a $ a-modules的数量。
We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a consequence, the number of support $τ$-tilting modules over the trivial extension $T(A)$ of a gentle tree algebra $A$ depends only on the number of simple $A$-modules.
