Explicit classifications of orbits in Jordan algebra and freudenthal vector space over the exceptional lie groups

Communications in Algebra

Volumn 34, Issue 1, 2006, Pages 197-217

  Shukuzawa, Osamu ^a  

^a NONE   (Japan)

Author keywords

Canonical form; Classification of orbits; Exceptional Lie group; Freudenthal vector space; Jordan algebra; Orbit; Quadratic form; Rank

Indexed keywords

EID: 30444440040     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927870500346206     Document Type: Article

References (19)

1. Freudenthal, H. (1951/1985). Oktaven, Ausnahmegruppen und Oktavengeometry. Math. Inst. Rijkuniv. te Utrecht (1985). Geom. Dedicata 19(1):7-63.
2. 8 zur Oktavenebene, I. Proc. Koninkl. Ned. Akad. Wetenschap. Proc. Ser. A57 Indag. Math. 16:218-230.
3. 7. J. Foc. Sci. Shinshu Univ. 15(1): 1-18.
4. 7(-133). J. Fac. Sci. Shinshu Univ. 15(2):47-52.
5. Jacobson, N. (1961). Some groups of transformations defined by Jordan algebras, III. J. Reine. Angew. Math. 207:61-85.
6. Krutelevich, S. (2002). On a canonical form of a 3 × 3 Hermitian matrix over the ring of integral split octonions. J. Algebra 253:276-295.
7. Krutelevich, S. (2003). Orbits of Exceptional Groups and Jordan Systems. Ph.D. thesis. Yale Univ.
8. 7. Tsukuba J. Math. 22(3):687-703.
9. c. Tsukuba J. Math. 23(2):229-234.
10. Shukuzawa, O. (2003a). Diagonalization of elements of Freudenthal R-vector space and split Freudenthal R-vector space. Tsukuba J. Math. 27(1):113-128.
11. Shukuzawa, O. (2003b). Orbit space of split Freudenthal vector space. Yokohama Math. J. 50(1):1-10.
12. 2. Preprint.
13. Shukuzawa, O., Yokota, I. (2003). Orbit spaces of Jordan algebras with respect to exceptional Lie groups and their orbit types. Yokohama Math. J. 50:11-21.
14. 6 and its involutive automorphisms. J. Math. Kyoto Univ. 20:447-473.
15. 6. Tsukuba J. Math. 14(1):185-223.
16. 7. Tsukuba J. Math. 14(2):379-404.
17. C. Proc. Symp. on non-associative algebras, Japan, pp. 353-359.
18. Yokota, I. (1992). Simple Lie groups of Exceptional Type (in Japanese). Kyoto: Gendai-Sugakusya.
19. Yokota, I. (2003). Compact Exceptional Lie Groups. Preprint.