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Quadratic automaton algebras and intermediate growth. (English) Zbl 1426.17003
Summary: 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 Gröbner basis with respect to any choice of generators and any choice of a well-ordering of monomials compatible withmultiplication. This answers a question of Ufnarovski.{
}Another result is a simple example (4 generators and 7 relations) of a quadratic algebra of intermediate growth.

MSC:
17A45 Quadratic algebras (but not quadratic Jordan algebras)
16P90 Growth rate, Gelfand-Kirillov dimension
16S37 Quadratic and Koszul algebras
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