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/
O'Donnell, Ryan ;
Pratt, Kevin
High-Dimensional Expanders from Chevalley Groups
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}
}
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Keywords: |
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High-dimensional expanders, simplicial complexes, group theory |
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Collection: |
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37th Computational Complexity Conference (CCC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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11.07.2022 |
