Academic Bibliography

 Search 200 years of publications by Ghent University researchers.
Advanced search
2 files | 1.05 MB
Add to list
  1. Search results
  2. High-dimensional expanders from Kac–M...

High-dimensional expanders from Kac–Moody–Steinberg groups

Laura Grave de Peralta and Inga Valentiner-Branth (UGent)
(2025) EUROPEAN JOURNAL OF COMBINATORICS. 126.
Author
Organization
Project
Abstract
High-dimensional expanders are a generalization of the notion of expander graphs to simplicial complexes and give rise to a variety of applications in computer science and other fields. We provide a general tool to construct families of bounded degree high-dimensional spectral expanders. Inspired by the work of Kaufman and Oppenheim, we use coset complexes over quotients of Kac-Moody-Steinberg groups of rank d + 1, dspherical and purely d-spherical. We prove that infinite families of such quotients exist provided that the underlying field is of size at least 4 and the Kac-Moody-Steinberg group is 2-spherical, giving rise to new families of bounded degree high-dimensional expanders. In case the generalized Cartan matrix we consider is affine, we recover the construction of O'Donnell and Pratt from 2022 (and thus also the one by Kaufman and Oppenheim) by considering Chevalley groups as quotients of affine Kac-Moody- Steinberg groups. Moreover, our construction applies to the case where the root system is of type in earlier works. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies. G G G2 G2, a case that was not covered

Downloads

  • Download
    HDXfromKMSarxiv.pdf
    • full text (Accepted manuscript)
    • |
    • open access
    • |
    • PDF
    • |
    • 437.85 KB
  • Download
    (...).pdf
    • full text (Published version)
    • |
    • UGent only
    • |
    • PDF
    • |
    • 616.57 KB

Citation

Please use this url to cite or link to this publication:

MLA
de Peralta, Laura Grave, and Inga Valentiner-Branth. “High-Dimensional Expanders from Kac–Moody–Steinberg Groups.” EUROPEAN JOURNAL OF COMBINATORICS, vol. 126, 2025, doi:10.1016/j.ejc.2025.104131.
APA
de Peralta, L. G., & Valentiner-Branth, I. (2025). High-dimensional expanders from Kac–Moody–Steinberg groups. EUROPEAN JOURNAL OF COMBINATORICS, 126. https://doi.org/10.1016/j.ejc.2025.104131
Chicago author-date
Peralta, Laura Grave de, and Inga Valentiner-Branth. 2025. “High-Dimensional Expanders from Kac–Moody–Steinberg Groups.” EUROPEAN JOURNAL OF COMBINATORICS 126. https://doi.org/10.1016/j.ejc.2025.104131.
Chicago author-date (all authors)
de Peralta, Laura Grave, and Inga Valentiner-Branth. 2025. “High-Dimensional Expanders from Kac–Moody–Steinberg Groups.” EUROPEAN JOURNAL OF COMBINATORICS 126. doi:10.1016/j.ejc.2025.104131.
Vancouver
1.
de Peralta LG, Valentiner-Branth I. High-dimensional expanders from Kac–Moody–Steinberg groups. EUROPEAN JOURNAL OF COMBINATORICS. 2025;126.
IEEE
[1]
L. G. de Peralta and I. Valentiner-Branth, “High-dimensional expanders from Kac–Moody–Steinberg groups,” EUROPEAN JOURNAL OF COMBINATORICS, vol. 126, 2025.
@article{01KC6XKM5P16ZA1VZ30A8SXGCE,
  abstract     = {{High-dimensional expanders are a generalization of the notion of expander graphs to simplicial complexes and give rise to a variety of applications in computer science and other fields. We provide a general tool to construct families of bounded degree high-dimensional spectral expanders. Inspired by the work of Kaufman and Oppenheim, we use coset complexes over quotients of Kac-Moody-Steinberg groups of rank d + 1, dspherical and purely d-spherical. We prove that infinite families of such quotients exist provided that the underlying field is of size at least 4 and the Kac-Moody-Steinberg group is 2-spherical, giving rise to new families of bounded degree high-dimensional expanders. In case the generalized Cartan matrix we consider is affine, we recover the construction of O'Donnell and Pratt from 2022 (and thus also the one by Kaufman and Oppenheim) by considering Chevalley groups as quotients of affine Kac-Moody- Steinberg groups. Moreover, our construction applies to the case where the root system is of type in earlier works. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies. G G G2 G2, a case that was not covered}},
  articleno    = {{104131}},
  author       = {{de Peralta, Laura Grave and Valentiner-Branth, Inga}},
  issn         = {{0195-6698}},
  journal      = {{EUROPEAN JOURNAL OF COMBINATORICS}},
  language     = {{eng}},
  pages        = {{26}},
  title        = {{High-dimensional expanders from Kac–Moody–Steinberg groups}},
  url          = {{http://doi.org/10.1016/j.ejc.2025.104131}},
  volume       = {{126}},
  year         = {{2025}},
}
Altmetric
View in Altmetric
Web of Science
Times cited: