Finitely presented quadratic algebras of intermediate growth

TL;DR

This paper presents two examples of finitely presented quadratic algebras that exhibit intermediate growth, expanding understanding of algebraic structures with specific growth behaviors.

Contribution

It introduces the first known examples of finitely presented quadratic algebras with intermediate growth, filling a gap in algebraic growth classification.

Findings

Provided two explicit examples of such algebras

Demonstrated intermediate growth behavior

Extended classification of algebraic growth types

Abstract

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.