Brauer configuration algebras defined by snake graphs and Kronecker modules

Abstract

<abstract><p>Recently, Çanakçi and Schroll proved that associated with a string module $ M(w) $ there is an appropriated snake graph $ \mathscr{G} $. They established a bijection between the corresponding perfect matching lattice $ \mathscr{L}(\mathscr{G}) $ of $ \mathscr{G} $ and the canonical submodule lattice $ \mathscr{L}(M(w)) $ of $ M(w) $. We introduce Brauer configurations whose polygons are defined by snake graphs in line with these results. The developed techniques allow defining snake graphs, which after suitable procedures, build Kronecker modules. We compute the dimension of the Brauer configuration algebras and their centers arising from the different processes. As an application, we estimate the trace norm of the canonical non-regular Kronecker modules and some families of trees associated with some snake graphs classes.</p></abstract>