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License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2022.18
URN: urn:nbn:de:0030-drops-165802
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16580/
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O'Donnell, Ryan ; Pratt, Kevin

High-Dimensional Expanders from Chevalley Groups

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LIPIcs-CCC-2022-18.pdf (0.9 MB)

Abstract

Let Φ be an irreducible root system (other than G₂) of rank at least 2, let ? be a finite field with p = char ? > 3, and let G(Φ,?) be the corresponding Chevalley group. We describe a strongly explicit high-dimensional expander (HDX) family of dimension rank(Φ), where G(Φ,?) acts simply transitively on the top-dimensional faces; these are λ-spectral HDXs with λ → 0 as p → ∞. This generalizes a construction of Kaufman and Oppenheim (STOC 2018), which corresponds to the case Φ = A_d. Our work gives three new families of spectral HDXs of any dimension ≥ 2, and four exceptional constructions of dimension 4, 6, 7, and 8.

BibTeX - Entry

@InProceedings{odonnell_et_al:LIPIcs.CCC.2022.18,
  author =	{O'Donnell, Ryan and Pratt, Kevin},
  title =	{{High-Dimensional Expanders from Chevalley Groups}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{18:1--18:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16580},
  URN =		{urn:nbn:de:0030-drops-165802},
  doi =		{10.4230/LIPIcs.CCC.2022.18},
  annote =	{Keywords: High-dimensional expanders, simplicial complexes, group theory}
}

Keywords: High-dimensional expanders, simplicial complexes, group theory
Collection: 37th Computational Complexity Conference (CCC 2022)
Issue Date: 2022
Date of publication: 11.07.2022

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