Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T13:10:49.397Z Has data issue: false hasContentIssue false
  • English
  • Français

On δ-Lie supertriple systems associated with (ε, δ)-Freudenthal-Kantor supertriple systems

Published online by Cambridge University Press:  20 January 2009

Noriaki Kamiya  and
Susumu Okubo
Noriaki Kamiya
Affiliation:
Center for Mathematical Sciences, University of Aizu, Aizuwakamatsu 965-8580, Japan
Susumu Okubo
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We will present an investigation of (ε, δ)-Freudenthal–Kantor supertriple systems that are intimately related to Lie supertriple systems and Lie superalgebras. We can also introduce a super analogue of Nijenhuis tensor and almost-complex structure in differential geometry.

Keywords

Freudenthal-Kantor supertriple systemLie supertriple systemLie superalgebra
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 243 - 260
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1. Berezin, F. A. and Leites, D. A., Supermanifolds, Dokl. Akad. Nauk SSSR 224 (1975), 1218–1222.Google Scholar
2. Faulkner, J. R. and Ferrar, J. C., Simple anti-Jordan pairs, Commun. Algebra 8 (1980), 993–1013.CrossRefGoogle Scholar
3. Freudenthal, H., Beziehungen der F7 and E8 zur Oktavenbener, I, II, Indag. Math. 16 (1954), 218–230, 363–386.CrossRefGoogle Scholar
4. Frölicher, A., Zur Differentialgeometrie der Komplexen Structuren, Math. Ann. 129 (1955), 50–95.CrossRefGoogle Scholar
5. Hein, W., A construction of Lie algebras by triple systems, Trans. Am. Math. Soc. 2051 (1975), 79–95.CrossRefGoogle Scholar
6. Helgason, S., Differential geometry, Lie groups and symmetric spaces (Academic, New York, 1978).Google Scholar
7. Jacobson, N., Lie and Jordan triple systems, Am. J. Math. 71 (1949), 149–170.CrossRefGoogle Scholar
8. Kamiya, N., A structure theory of Freudenthal–Kantor triple systems, J. Alg. 110 (1987), 108–123.CrossRefGoogle Scholar
9. Kamiya, N., A construction of anti-Lie triple systems from a class of triple systems, Mem. Fac. Sci. Shimane University 22 (1988), 51–62.Google Scholar
10. Kamiya, N., A structure theory of Freudenthal–Kantor triple systems, II, Commun. Math., Univ. Sancti Pauli 38 (1989), 41–60.Google Scholar
11. Kamiya, N., The construction of all simple Lie algebras over C from balanced Freudenthal–Kantor triple system, in Contributions to General Algebra, vol. 7, pp. 205–213 (Hölder–Pichler–Tempsky, Wien, B. G. Teubner, Stuttgart, 1991).Google Scholar
12. kamiya, N., On Freudenthal–Kantor triple systems and generalized structurable algebras, Nonassociative algebras and its applications, In Mathematics and its Applications, vol. 303, pp. 198–203 (Kluwer, Dordrecht, 1994).Google Scholar
13. Kamiya, N., The nil radical for Lie or anti-Lie triple systems, J. Alg. 156 (1993), 226–232.CrossRefGoogle Scholar
14. Kantor, I. L., Models of exceptional Lie algebras, Sov. Math. Dokl. 14 (1973), 254–258.Google Scholar
15. Kobayashi, S. and Nomizu, K., Foundations of differential geometry, I and II (Inter-science, New York, 1963).Google Scholar
16. Newlander, A. and Nirenberg, L., Complex analytic coordinates in almost complex manifolds, Ann. Math. 65 (1957), 391–404.CrossRefGoogle Scholar
17. Okubo, S., Nijenhuis tensor, BRST cohomology and related algebras, Alg. Group Geom. 6 (1989), 65–112.Google Scholar
18. Okubo, S., Triple products and Yang–Baxter equation, I and II, J. Math. Phys. 34 (1993), 3273–3291 (I), 3292–3315 (II).CrossRefGoogle Scholar
19. Okubo, S., Introduction to octonion and other non–associative algebras in physics (Cambridge University press, 1995).CrossRefGoogle Scholar
20. Okubo, S. and Kamiya, N., Quasi-classical Lie-superalgebra and Lie supertriple systems, University of Rochester report UR–1462 (1996).Google Scholar
21. Okubo, S. and Kamiya, N., Jordan–Lie superalgebras and Jordan–Lie triple systems, J. Alg. 198 (1997), 388–411.CrossRefGoogle Scholar
22. Rothstein, M., Deformations of complex supermanifolds, Proc. Am. Math. Soc. 95 (1985), 255–266.CrossRefGoogle Scholar
23. Scheunert, M., The theory of Lie superalgebras (Springer, Berlin, 1979).CrossRefGoogle Scholar
24. Svinolupov, S. I., Generalized Schrödinger equations and Jordan pairs, Commun. Math. Phys. 143 (1992), 559–575.CrossRefGoogle Scholar
25. Yamaguti, K. and Ono, A., On representation of Freudenthal–Kantor triple systems U(ε,δ), Bull. Fac. School, Ed. Hiroshima University, Part II 7 (1984), 43–51.Google Scholar