On a certain invariant of the groups of type E6 and E7

Ichiro SATAKE

doi:10.2969/jmsj/02010322

On a certain invariant of the groups of type E₆ and E₇

Ichiro SATAKE

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JOURNAL FREE ACCESS

1968 Volume 20 Issue 1-2 Pages 322-335

DOI https://doi.org/10.2969/jmsj/02010322

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Published: 1968 Received: August 10, 1967 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor S. Iyanaga on his 60th birthday

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. P. Allen, Jordan algebras and Lie algebras of type D₄ Bull. Amer. Math. Soc., 72 (1966), 65-67.
2) E. Cartan, Sur la structure des groupes de transformations finis et continus (Thèse), Paris, 1894; Oeuvres complètes, Vol. 1, Paris, Gauthier-Villars, 1952, 137-287.
3) E. Cartan, Les groupes projectifs qui ne laissent invariante aucune multiplicité plane, Bull. Soc. Math. France, 4 (1913), 53-96; Oeuvres complètes, Vol. 1, Paris, Gauthier-Villars, 355-398.
4) E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Mat. Sb. N. S., 30 (72) (1952), 349-462; Amer. Math. Soc. Transl., Ser. 2, 6 (1957), 111-244.
5) J. C. Ferrar, On Lie algebras of type E₆, Bull. Amer. Math. Soc., 73 (1967), 151-155.
6) M. Kneser, Galois-Kohomologie halbeinfacher algebraischer Gruppen über p-adischen Körpern, II, Math. Zeit., 89 (1965), 250-272.
7) M. Koecher and H. Braun, Jordan-Algebren, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
8) I. Satake, On the theory of reductive algebraic groups over a perfect field, J. Math. Soc. Japan, 15 (1963), 210-235.
9) I. Satake, Symplectic representations of algebraic groups satisfying a certain analyticity condition, Acta Math., 117 (1967), 215-279.
10) T. Springer, Oktaven, Jordan-Algebren and Ausnahmegruppen, Lecture Note, Göttingen, 1963.
11) J. Tits, Classification of algebraic semisimple groups, Proc. of Symposia in pure Math., Vol. 9 (1966), 33-62.
12) J. Tits, Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionelles, I. Construction, Indag. Math., 28 (=Proc. Kon. Ned. Akad. Wet. Ser. A, 69) (1966), 223-237.
13) R. D. Schafer, An introduction to nonassociative algebras, Academic Press, New York and London, 1966.

Right : [1] H. P. Allen, Jordan algebras and Lie algebras of type D₄ Bull. Amer. Math. Soc., 72 (1966), 65-67.
[2] E. Cartan, Sur la structure des groupes de transformations finis et continus (Thèse), Paris, 1894; Oeuvres complètes, Vol. 1, Paris, Gauthier-Villars, 1952, 137-287.
[3] E. Cartan, Les groupes projectifs qui ne laissent invariante aucune multiplicité plane, Bull. Soc. Math. France, 4 (1913), 53-96; Oeuvres complètes, Vol. 1, Paris, Gauthier-Villars, 355-398.
[4] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Mat. Sb. N. S., 30 (72) (1952), 349-462; Amer. Math. Soc. Transl., Ser. 2, 6 (1957), 111-244.
[5] J. C. Ferrar, On Lie algebras of type E₆, Bull. Amer. Math. Soc., 73 (1967), 151-155.
[6] M. Kneser, Galois-Kohomologie halbeinfacher algebraischer Gruppen über p-adischen Körpern, II, Math. Zeit., 89 (1965), 250-272.
[7] M. Koecher and H. Braun, Jordan-Algebren, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
[8] I. Satake, On the theory of reductive algebraic groups over a perfect field, J. Math. Soc. Japan, 15 (1963), 210-235.
[9] I. Satake, Symplectic representations of algebraic groups satisfying a certain analyticity condition, Acta Math., 117 (1967), 215-279.
[10] T. Springer, Oktaven, Jordan-Algebren und Ausnahmegruppen, Lecture Note, Göttingen, 1963.
[11] J. Tits, Classification of algebraic semisimple groups, Proc. of Symposia in pure Math., Vol. 9 (1966), 33-62.
[13] R. D. Schafer, An introduction to nonassociative algebras, Academic Press, New York and London, 1966.

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

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