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On the subsemigroup complex of an aperiodic Brandt semigroup

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Abstract

We introduce the subsemigroup complex of a finite semigroup S as a (boolean representable) simplicial complex defined through chains in the lattice of subsemigroups of S. We present a research program for such complexes, illustrated through the particular case of combinatorial Brandt semigroups. The results include alternative characterizations of faces and facets, asymptotical estimates on the number of facets, or establishing when the complex is pure or a matroid.

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Acknowledgements

Stuart Margolis acknowledges support from the Binational Science Foundation (BSF) of the United States and Israel, Grant Number 2012080. John Rhodes acknowledges support from the Simons Foundation. Pedro V. Silva was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.

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Authors and Affiliations

  1. Department of Mathematics, Bar Ilan University, 52900, Ramat Gan, Israel

    Stuart Margolis

  2. Department of Mathematics, University of California-Berkeley, Berkeley, CA, 94720, USA

    John Rhodes

  3. Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre 687, 4169-007, Porto, Portugal

    Pedro V. Silva

Authors
  1. Stuart Margolis
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  2. John Rhodes
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  3. Pedro V. Silva
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Correspondence to Stuart Margolis.

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Communicated by Benjamin Steinberg.

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Margolis, S., Rhodes, J. & Silva, P.V. On the subsemigroup complex of an aperiodic Brandt semigroup. Semigroup Forum 97, 7–31 (2018). https://doi.org/10.1007/s00233-018-9927-4

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  • DOI: https://doi.org/10.1007/s00233-018-9927-4

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