An introduction to a supersymmetric graph algebra

TL;DR

This paper introduces a new supersymmetric graph algebra, extending Leavitt path algebras, and explores its basis and growth properties, contributing to the mathematical understanding of algebraic structures with supersymmetry.

Contribution

It proposes a novel supersymmetric analogue of Leavitt path algebras and characterizes their basis and polynomial growth conditions.

Findings

Established a basis for the supersymmetric graph algebra

Characterized conditions for polynomial growth

Extended algebraic structures with supersymmetry

Abstract

In this paper we propose a graph superalgebra which is the supersymmetric analogue of Leavitt path algebras. We find a basis for these superalgebras and characterize when they have polynomial growth.