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Quadratic automaton algebras and intermediate growth
- Source :
- J.Combinatorial Algebra, V2, N2, 2018, pp. 147-167
- Publication Year :
- 2017
-
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.<br />Comment: To appear in Journal of Cobinatorial Algebra
- Subjects :
- Mathematics - Rings and Algebras
17A45, 16A22
Subjects
Details
- Database :
- arXiv
- Journal :
- J.Combinatorial Algebra, V2, N2, 2018, pp. 147-167
- Publication Type :
- Report
- Accession number :
- edsarx.1705.09972
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4171/JCA/2-2-2