Special Session 44: The theory of cluster algebras and its applications

Derived equivalences between one-branch extensions of rectangles

Yanan Lin
Xiamen University
Peoples Rep of China
Co-Author(s):    Qiang Dong, Yanan Lin and Shiquan Ruan
Abstract:
This is joint work with Qiang Dong and Shiquan Ruan. 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.