Quadratic automaton algebras and intermediate growth
Rings and Algebras
2020-08-04 v2
Abstract
We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis with respect to any choice of generators and any choice of a well-ordering of monomials compatible with multiplication. This answers a question of Ufnarovski. Another result is a simple example (4 generators and 7 relations) of a quadratic algebra of intermediate growth.
Keywords
Cite
@article{arxiv.1705.09972,
title = {Quadratic automaton algebras and intermediate growth},
author = {Natalia Iyudu and Stanislav Shkarin},
journal= {arXiv preprint arXiv:1705.09972},
year = {2020}
}
Comments
To appear in Journal of Cobinatorial Algebra