Advanced search
Publication Cover
Communications in Algebra Volume 52, 2024 - Issue 8
Submit an article Journal homepage
58
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Octonions, Albert vectors and the group E6(F)

John N. Braya Independent Scholar
,
Yegor Stepanovb School of Mathematical Sciences, Queen Mary University of London, London, United KingdomCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0009-0002-3491-0435
ORCID Icon &
Robert A. Wilsonb School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Pages 3461-3489 | Received 07 Nov 2023, Accepted 13 Feb 2024, Published online: 06 Mar 2024

References

  • Aschbacher, M. E. (1987). The 27-dimensional module for E6, I. Invent. Math. 89:159–195. DOI: 10.1007/BF01404676.
  • Aschbacher, M. E. (1988). The 27-dimensional module for E6, II. J. London Math. Soc. 37:275–293. DOI: 10.1112/jlms/s2-37.2.275.
  • Aschbacher, M. E. (1990). The 27-dimensional module for E6, III. Trans. Amer. Math. Soc. 321:45–84. DOI: 10.2307/2001591.
  • Aschbacher, M. E. (1990). The 27-dimensional module for E6, IV. J. Algebra 131:23–39. DOI: 10.1016/0021-8693(90)90164-J.
  • Aschbacher, M. E. The 27-dimensional module for E6, V, unpublished.
  • Chevalley, C. (1955). Sur certains groupes simples. Tôhoku Math. J. 7:14–66.
  • Dickson, L. E. (1901). A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface. Q. J. Pure Appl. Math. 33:145–173.
  • Dickson, L. E. (1908). A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface (second paper). Q. J. Pure Appl. Math. 33:205–209.
  • Jacobson, N. (1959). Some groups of transformations defined by Jordan algebras. I. J. Reine Angew. Math. 201:178–195. DOI: 10.1515/crll.1959.201.178.
  • Jacobson, N. (1960). Some groups of transformations defined by Jordan algebras. II. Groups of type F4. J. Reine Angew. Math. 204:74–98.
  • Jacobson, N. (1961). Some groups of transformations defined by Jordan algebras. III. Groups of type E6I . J. Reine Angew. Math. 207:61–85.
  • Cohen, A. M., Cooperstein, B. N. (1988). The 2-spaces of the standard E6(q) -module. Geom. Dedicata 25:467–480.
  • Springer, T. A., Veldkamp, F. D. (1999). Octonions, Jordan Algebras and Exceptional Groups. Spinger Monographs in Mathematics. Berlin: Springer.
  • Wilson, R. A. Albert algebras and construction of the finite simple groups F4(q),E6(q) and 2E6(q) and their generic covers. arXiv:1310.5886
  • Wilson, R. A. (2009). The Finite Simple Groups, Springer GTM 251. London: Springer.
  • Schafer, R. D. (1966). An Introduction to Nonassociative Algebras. New York: Academic Press.
  • Taylor, D. E. (1992). The Geometry of the Classical Groups, Sigma Series in Pure Mathematics. Berlin: Heldermann.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.