Year: 2015
Type: preprint
Abstract: The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g. that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.
Source: arXiv (Cornell University)
Authors: Li, Fang, Ye, Chang
Institution: Zhejiang University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2180829774