Quadratic automaton algebras and intermediate growth

Natalia Iyudu; Stanislav Shkarin

doi:10.4171/JCA/2-2-2

Quadratic automaton algebras and intermediate growth

Natalia Iyudu, Stanislav Shkarin

School of Mathematics and Physics

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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.

Original language	English
Pages (from-to)	147-167
Journal	Journal of Combinatorial Algebra
Volume	2
Issue number	2
DOIs	https://doi.org/10.4171/JCA/2-2-2
Publication status	Published - 08 May 2018

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Quadratic automaton algebras and intermediate growth
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Stanislav Shkarin
- s.shkarinqub.acuk
- School of Mathematics and Physics - Lecturer
- Mathematical Sciences Research Centre
Person: Academic

Cite this

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Quadratic automaton algebras and intermediate growth

Abstract

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Stanislav Shkarin

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