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The Gelfand–Kirillov dimension of Hecke–Kiselman algebras

  • Magdalena Wiertel ORCID logo EMAIL logo
Published/Copyright: January 27, 2023

Abstract

Hecke–Kiselman algebras A Θ , over a field 𝕂 , associated to finite oriented graphs Θ are considered. It has been known that every such algebra is an automaton algebra in the sense of Ufranovskii. In particular, its Gelfand–Kirillov dimension is an integer if it is finite. In this paper, a numerical invariant of the graph Θ that determines the dimension of A Θ is found. Namely, we prove that the Gelfand–Kirillov dimension of A Θ is the sum of the number of cyclic subgraphs of Θ and the number of oriented paths of a special type in the graph, each counted certain specific number of times.


Communicated by Manfred Droste


Funding statement: This work is supported by grant 2021/41/N/ST1/03082 of the National Science Centre (Poland). For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.

Acknowledgements

I am very grateful to Jan Okniński for careful reading and many suggestions on the earlier versions of the paper, as well as his continuous support. I would also like to thank Arkadiusz Męcel for fruitful discussions about the research topic.

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Received: 2022-07-08
Revised: 2022-12-21
Published Online: 2023-01-27
Published in Print: 2023-03-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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