A geometry for $E_{7}$
HTML articles powered by AMS MathViewer
- by John R. Faulkner PDF
- Trans. Amer. Math. Soc. 167 (1972), 49-58 Request permission
Abstract:
A geometry is defined by the 56-dimensional representation $\mathfrak {M}$ of a Lie algebra of type ${E_7}$. Every collineation is shown to be induced by a semisimilarity of $\mathfrak {M}$, and the image of the automorphism group of $\mathfrak {M}$ in the collineation group is shown to be simple.References
- Jean Dieudonné, La géométrie des groupes classiques, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (French). Seconde édition, revue et corrigée. MR 0158011, DOI 10.1007/978-3-662-59144-4
- John R. Faulkner, A construction of Lie algebras from a class of ternary algebras, Trans. Amer. Math. Soc. 155 (1971), 397–408. MR 294424, DOI 10.1090/S0002-9947-1971-0294424-X
- John R. Faulkner, Octonion planes defined by quadratic Jordan algebras, Memoirs of the American Mathematical Society, No. 104, American Mathematical Society, Providence, R.I., 1970. MR 0271180
- Hans Freudenthal, Beziehungen der $\mathfrak {E}_7$ und $\mathfrak {E}_8$ zur Oktavenebene. IV, Nederl. Akad. Wetensch. Proc. Ser. A. 58 (1955), 277–285 = Indag. Math. 17, 277–285 (1955) (German). MR 0068551, DOI 10.1016/S1385-7258(55)50039-4
- Max Koecher, Über eine Gruppe von rationalen Abbildungen, Invent. Math. 3 (1967), 136–171 (German). MR 214630, DOI 10.1007/BF01389742
- Kevin McCrimmon, The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras, Trans. Amer. Math. Soc. 139 (1969), 495–510. MR 238916, DOI 10.1090/S0002-9947-1969-0238916-9
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 167 (1972), 49-58
- MSC: Primary 50D30; Secondary 20H15
- DOI: https://doi.org/10.1090/S0002-9947-1972-0295205-4
- MathSciNet review: 0295205