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The socle series of a Leavitt path algebra

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Abstract

We investigate the ascending Loewy socle series of Leavitt path algebras L K (E) for an arbitrary graph E and field K. We classify those graphs E for which L K (E) = S λ for some element S λ of the Loewy socle series. We then show that for any ordinal λ there exists a graph E so that the Loewy length of L K (E) is λ. Moreover, λ ≤ ω 1 (the first uncountable ordinal) if E is a row-finite graph.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Colorado Springs, CO, 80918, USA

    Gene Abrams & Kulumani M. Rangaswamy

  2. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain

    Mercedes Siles Molina

Authors
  1. Gene Abrams
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  2. Kulumani M. Rangaswamy
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  3. Mercedes Siles Molina
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Corresponding author

Correspondence to Gene Abrams.

Additional information

The first author is partially supported by the U.S. National Security Agency under grant number H89230-09-1-0066. The third author is partially supported by the Spanish MEC and Fondos FEDER through projects MTM2007-60333 and MTM2010-15223, and jointly by the Junta de Andalucía and Fondos FEDER through projects FQM-336 and FQM-2467. This work was initiated while the third author was hosted as a Research Visitor by the Department of Mathematics at the University of Colorado at Colorado Springs. She thanks this host center for its warm hospitality and support.

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Abrams, G., Rangaswamy, K.M. & Molina, M.S. The socle series of a Leavitt path algebra. Isr. J. Math. 184, 413–435 (2011). https://doi.org/10.1007/s11856-011-0074-9

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  • DOI: https://doi.org/10.1007/s11856-011-0074-9

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