Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The compact exceptional Lie algebra $\mathfrak g^c_2$ as a twisted ring group
HTML articles powered by AMS MathViewer

by Cristina Draper;
Proc. Amer. Math. Soc. 152 (2024), 3679-3688
DOI: https://doi.org/10.1090/proc/16821
Published electronically: July 17, 2024

Abstract:

A new highly symmetrical model of the compact Lie algebra $\mathfrak {g}^c_2$ is provided as a twisted ring group for the group $\mathbb {Z}_2^3$ and the ring $\mathbb {R}\oplus \mathbb {R}$. The model is self-contained and can be used without previous knowledge on roots, derivations on octonions or cross products. In particular, it provides an orthogonal basis with integer structure constants, consisting entirely of semisimple elements, which is a generalization of the Pauli matrices in $\mathfrak {su}(2)$ and of the Gell-Mann matrices in $\mathfrak {su}(3)$. As a bonus, the split Lie algebra $\mathfrak {g}_2$ is also seen as a twisted ring group.
References
Similar Articles
Bibliographic Information
  • Cristina Draper
  • Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Spain
  • MR Author ID: 651907
  • ORCID: 0000-0002-2998-7473
  • Email: cdf@uma.es
  • Received by editor(s): July 22, 2023
  • Received by editor(s) in revised form: February 4, 2024, and February 9, 2024
  • Published electronically: July 17, 2024
  • Additional Notes: This work was supported by the Spanish Ministerio de Ciencia e Innovación through projects PID2019-104236GB-I00/AEI/10.13039/501100011033 and PID2020-118452GB-I00, all of them with FEDER funds, and by the group FQM-336 by Junta de Andalucía
  • Communicated by: Sarah Witherspoon
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3679-3688
  • MSC (2020): Primary 17B25, 16S35; Secondary 20C05, 17B70
  • DOI: https://doi.org/10.1090/proc/16821
  • MathSciNet review: 4781965