Quadratic automaton algebras and intermediate growth

Natalia Iyudu, Stanislav Shkarin

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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 languageEnglish
Pages (from-to)147-167
JournalJournal of Combinatorial Algebra
Volume2
Issue number2
DOIs
Publication statusPublished - 08 May 2018

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