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On Leavitt Path Algebras of Hopf Graphs

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Abstract

In this paper, we provide the structure of Hopf graphs associated to pairs \((G, \mathfrak {r})\) consisting of groups G together with ramification datas \(\mathfrak {r}\) and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data \(\mathfrak {r}\) and G.

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Acknowledgements

The authors were supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant 101.04-2020.01. We also take an opportunity to express their deep gratitude to the anonymous referee for extremely careful reading, highly professional working with our manuscript, and quite valuable suggestions.

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Authors and Affiliations

  1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    T. G. Nam

  2. Faculty of Mathematics - Informatics Teacher Education, Dong Thap University, Dong Thap, Vietnam

    N. T. Phuc

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  1. T. G. Nam
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  2. N. T. Phuc
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Correspondence to N. T. Phuc.

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Nam, T.G., Phuc, N.T. On Leavitt Path Algebras of Hopf Graphs. Acta Math Vietnam 48, 533–549 (2023). https://doi.org/10.1007/s40306-023-00511-7

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  • DOI: https://doi.org/10.1007/s40306-023-00511-7

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