Context-free languages and associative algebras with algebraic Hilbert series
Rings and Algebras
2021-04-23 v1
Abstract
In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct a class of finitely presented associative algebras related to a family of context-free languages. This allows us to connect the Hilbert series of these algebras with the generating functions of such languages. In particular, we obtain a class of finitely presented graded algebras with non-rational algebraic Hilbert series.
Keywords
Cite
@article{arxiv.2001.09112,
title = {Context-free languages and associative algebras with algebraic Hilbert series},
author = {Roberto La Scala and Dmitri Piontkovski},
journal= {arXiv preprint arXiv:2001.09112},
year = {2021}
}
Comments
11 pages