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 wellordering 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.
Another result is a simple example (4 generators and 7 relations) of a quadratic algebra of intermediate growth.
Original language  English 

Pages (fromto)  147167 
Journal  Journal of Combinatorial Algebra 
Volume  2 
Issue number  2 
DOIs  
Publication status  Published  08 May 2018 
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Stanislav Shkarin
Person: Academic