Projective geometry of Freudenthal's varieties of certain type

Michigan Mathematical Journal

Volumn 52, Issue 3, 2004, Pages 515-542

  Kaji, Hajime ^a   Yasukura, Osami ^b  

^a WASEDA UNIVERSITY   (Japan)

^b UNIVERSITY OF FUKUI   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11044226013     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1100623411     Document Type: Article

References (30)

1. H. Asano, On triple systems, Yokohama City Univ. Ronso, Ser. Natural Sci. 27 (1975), 7-31.
2. _, On points and planes in symplectic triple systems, preprint.
3. _, Symplectic triple systems and simple Lie algebras, RIMS Kokyu-roku, Kyoto Univ. 308 (1977), 41-54.
4. _, A characterization theorem in symplectic triple systems, personal communication to O. Yasukura, May 8, 1989, Yokohama City Univ.
5. _, On simple symplectic triple systems, personal communication to O. Yasukura, July 3, 2000, Yokohama City Univ.
6. N. Bourbaki, Éléments de Mathématique, Groupes et algèbres de Lie, Hermann, Paris, 1968.
7. L. Ein and N. Shepherd-Barron, Some special Cremona transformations, Amer. J. Math. 111 (1989), 783-800.
8. J. R. Faulkner, A construction of Lie algebras from a class of ternary algebras, Trans. Amer. Math. Soc. 155 (1971), 397-408.
9. J. C. Ferrar, Strictly regular elements in Freudenthal triple systems, Trans. Amer. Math. Soc. 174 (1972), 313-331.
10. H. Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964), 145-190.
11. T. Fujita and J. Roberts, Varieties with small secant varieties: The extremal case, Amer. J. Math. 103 (1981), 953-976.
12. W. Fulton and J. Harris, Representation theory: A first course, Grad. Texts in Math., 129, Springer-Verlag, New York, 1991.
13. S. J. Harris, Some irreducible representations of exceptional algebraic groups, Amer. J. Math. 93 (1971), 75-106.
14. W. Hein, A construction of Lie algebras by triple systems, Trans. Amer. Math. Soc. 205 (1975), 79-95.
15. J. Igusa, A classification of spinors up to dimension twelve, Amer. J. Math. 92 (1970), 997-1028.
16. H. Kaji, M. Ohno, and O. Yasukura, Adjoint varieties and their secant varieties, Indag. Math. (N.S.) 10 (1999), 45-57.
17. H. Kaji and O. Yasukura, Tangent loci and certain linear sections of adjoint varieties, Nagoya Math. J. 158 (2000), 63-72.
18. _, Secants, tangents and the homogeneity of Freudenthal varieties of certain type, preprint, Preprint Series A2001/29, IMPA Preprint Server.
19. T. Kimura, The b-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, Nagoya Math. J. 85 (1982), 1-80.
20. K. Meyberg, Eine Theorie der Freudenthalschen Tripelsysteme, I, II, Indag. Math. 30 (1968), 162-190.
21. S. Mukai, Projective geometry of homogeneous spaces, Proc. Sympos. Algebraic Geometry, Waseda Univ. (1994), pp. 1-52 (in Japanese).
22. M. Muro, Some prehomogeneous vector spaces with relative invariants of degree four and the formula of the Fourier transforms, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 70-74.
23. Y. Omoda, On Freudenthal's geometry and generalized adjoint varieties, J. Math. Kyoto Univ. 40 (2000), 137-153.
24. J. G. Semple and L. Roth, Introduction to algebraic geometry, Oxford Univ. Press, New York, 1949.
25. T. Springer, Linear algebraic groups, Algebraic geometry IV (A. N. Parshin and I. R. Shafarevich, eds.), Encyclopedia Math. Sci., 55, pp. 1-121, Springer-Verlag, Berlin, 1994.
26. N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan J. Math. (N.S.) 2 (1976), 131-190.
27. E. B. Vinberg, The Weyl group of a graded Lie algebra, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), 488-526.
28. K. Yamaguti and H. Asano, On Freudenthal's construction of exceptional Lie algebras, Proc. Japan Acad. Ser. A Math. Sci. 51 (1975), 253-258.
29. O. Yasukura, Symplectic triple systems and graded Lie algebras, Nonassociative algebras and related topics (Hiroshima, 1990), pp. 345-351, World Scientific, River Edge, NJ, 1991.
30. F. L. Zak, Tangents and secants of algebraic varieties, Transl. Math. Monogr., 127, Amer. Math. Soc., Providence, RI, 1993.