  In 2017, Green and Schroll introduced a generalization of Brauer graph
algebras which they call Brauer configuration algebras. In the present paper,
we further generalize Brauer configuration algebras to fractional Brauer
configuration algebras by generalizing Brauer configurations to fractional
Brauer configurations. The fractional Brauer configuration algebras are locally
bounded but neither finite-dimensional nor symmetric in general. We show that
if the fractional Brauer configuration is of type S (resp. of type MS), then
the corresponding fractional Brauer configuration algebra is a locally bounded
Frobenius algebra (resp. a locally bounded special multiserial Frobenius
algebra). Moreover, we show that over an algebraically closed field, the class
of finite-dimensional indecomposable representation-finite fractional Brauer
configuration algebras in type S coincides with the class of basic
indecomposable finite-dimensional standard representation-finite self-injective
algebras.
