Unitary groups in projective octave planes
Veldkamp, F. D.
Compositio Mathematica, Tome 20 (1968), p. 213-258 / Harvested from Numdam
Publié le : 1968-01-01
@article{CM_1968__19_3_213_0,
     author = {Veldkamp, F. D.},
     title = {Unitary groups in projective octave planes},
     journal = {Compositio Mathematica},
     volume = {20},
     year = {1968},
     pages = {213-258},
     mrnumber = {236815},
     zbl = {0195.50402},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1968__19_3_213_0}
}
Veldkamp, F. D. Unitary groups in projective octave planes. Compositio Mathematica, Tome 20 (1968) pp. 213-258. http://gdmltest.u-ga.fr/item/CM_1968__19_3_213_0/

Artin, E., [1] Geometric Algebra. Interscience, New York 1957. | MR 82463 | Zbl 0077.02101

Van Der Blij, F. and T.A. Springer, [2] The arithmetics of octaves and of the group G2. Proc. Kon. Ned. Akad. Wet. A, 62(- Indag. Math. 21), 406-418 (1959). | Zbl 0089.25803

[3] Octaves and triality. Nieuw Archief Wisk. (3) 8, 158-169 (1960). | Zbl 0127.11804

Braun, H. und M. Koecher, [4] Jordan-Algebren. Springer, Berlin 1966. | MR 204470 | Zbl 0145.26001

Chevalley, C., [5] Sur certains groupes simples. Tôhoku Math. J. (2) 7, 14-66 (1955). | Zbl 0066.01503

Dieudonné, J., [6] La géométrie des groupes classiques. 2e édition. Springer, Berlin 1963. | MR 158011 | Zbl 0111.03102

Ferrar, J.C., [7] On Lie algebras of type E6. Dissertation Yale University 1966.

Freudenthal, H., [8] Oktaven, Ausnahmegruppen und Oktavengeometrie. Utrecht 1951 (Neuauflage 1960). | MR 44533 | Zbl 0056.25905

Jacobson, N., [9] Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo II, 7, 55-80 (1958). | MR 101253 | Zbl 0083.02702

[10] Some groups of transformations defined by Jordan algebras, I, J. reine angew. Math. 201, 178-195 (1959);II, ibid. 204, 74-98 (1960);III, ibid. 207, 61-95 (1961). | Zbl 0084.03601

[11] Lie algebras. Interscience, New York 1962. | Zbl 0121.27504

[12] Triality and Lie algebras of type D4. Rend. Circ. Mat. Palermo II, 13, 129-153 (1964). | Zbl 0144.27103

Moufang, R., [13] Zur Struktur von Alternativkörpern. Math. Ann. 110, 416-430 (1934). | JFM 60.0093.02 | Zbl 0010.00403

Ono, T., [14] Sur les groupes de Chevalley. J. Math. Soc. Japan 10, 307-313 (1958). | Zbl 0085.01705

Seligman, G., [15] On automorphisms of Lie algebras of classical type. III. Transactions AMS 97, 286-316 (1960). | Zbl 0097.02202

Soda, D., [16] Groups of type D4 defined by Jordan algebras. Dissertation Yale University 1964.

[17] Some groups of type D4 defined by Jordan algebras. J. reine angew. Math. 223, 150-163 (1966). | MR 201487 | Zbl 0142.26303

Springer, T.A., [18] On a class of Jordan algebras. Proc. Kon. Ned. Akad. Wet. A, 62( - Indag. Math. 21), 254-264 (1959). | Zbl 0092.03701

[19] The projective octave plane. Ibid. A, 63(- Indag. Math. 22), 74-101 (1960). | Zbl 0131.36901

[20] The classification of reduced exceptional simple Jordan algebras. Ibid. 414-422 (1960). | MR 147520 | Zbl 0098.02901

[21] On the geometric algebra of octave planes. Ibid. A, 65( - Indag. Math. 24), 451-468 (1962). | Zbl 0113.35903

Springer, T.A. and F.D. Veldkamp, [22] Elliptic and hyperbolic octave planes. Ibid. A, 66( - Indag. Math. 25), 413-451 (1963). | Zbl 0127.11503

Steinberg, R., [23] Variations on a theme of Chevalley. Pacific J. Math. 9, 875-891 (1959). | Zbl 0092.02505

[24] The simplicity of certain groups. Ibid. 10, 1039-1041 (1960). | MR 123646 | Zbl 0093.03503

[25] Automorphisms of classical Lie algebras. Ibid. 11, 1119-1129 (1961). | MR 143845 | Zbl 0104.02905

Tits, J., [26] Le plan projectif des octaves et les groupes de Lie exceptionnels. Ac. Roy. Belg., Bull. Cl. Sci. 39, 309-329 (1953). | MR 54608 | Zbl 0050.25803

[27] Le plan projectif des octaves et les groupes exceptionnels E6 et E7. Ibid. 40, 29-40 (1954). | Zbl 0055.13903

[28] Les "formes réelles" des groupes de type E6. Sém. Bourbaki 1957-1958, exposé 162. | Numdam | Zbl 0084.25804

[29] Algebraic and abstract simple groups. Ann. Math. 80, 313-329 (1964). | MR 164968 | Zbl 0131.26501

Wonenburger, María J., [30] The Clifford algebra and the group of similitudes. Can. J. Math. 14, 45-59 (1962). | MR 132112 | Zbl 0100.25402

[31] Triality principle for semisimilarities. J. of Algebra 1, 335-341 (1964). | MR 170960 | Zbl 0126.06001