论文标题
“矩形”的单分支扩展之间的派生等价
Derived equivalences between one-branch extensions of "rectangles"
论文作者
论文摘要
在本文中，我们研究了由“矩形”的单一分支扩展产生的代数。有四种不同的方式来形成此类扩展，并且所有四种发病率代数均已得出等效。我们通过在Nakayama代数中倾斜复合物为所有人提供实现。作为申请，我们获得了Nakayama代数一半的Coxeter多项式的显式公式（即Nakayama代数$ n（n，r）$，$ 2R \ geq n+2 $）。同时，已经发现了Nakayama代数$ n（2r-1，r）$和$ n（2r-1，r+1）$之间的意外派生对等。
In this paper we investigate the incidence algebras arising from one-branch extensions of "rectangles". There are four different ways to form such extensions, and all four kinds of incidence algebras turn out to be derived equivalent. We provide realizations for all of them by tilting complexes in a Nakayama algebra. As an application, we obtain the explicit formulas of the Coxeter polynomials for a half of Nakayama algebras (i.e., the Nakayama algebras $N(n,r)$ with $2r\geq n+2$). Meanwhile, an unexpected derived equivalence between Nakayama algebras $N(2r-1,r)$ and $N(2r-1,r+1)$ has been found.
