Quaternionic and octonionic spinors. A classification

Journal of High Energy Physics

Volumn 7, Issue 4, 2003, Pages 901-928

  Carrion, Hector Leny ^a   Rojas, Moises ^a   Toppan, Francesco ^a  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

Author keywords

Differential and Algebraic Geometry; Extended Supersymmetry; M Theory; Space Time Symmetries

Indexed keywords

EID: 21444452687     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/04/040     Document Type: Article

References (35)

1. E. Bergshoeff and A. Van Proeyen, The many faces of OSp(1|32), Class. and Quant. Grav. 17 (2000) 3277 [hep-th/0003261].
2. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, Cambridge University Press, Cambridge 1987.
3. M.F. Atiyah, R. Bott and A. Shapiro, Clifford algebras, Topology (Suppl. 1) 3 (1964) 3.
4. T. Kugo and P.K. Townsend, Supersymmetry and the division algebras, Nucl. Phys. B 221 (1983) 357.
5. S. Okubo, Real representations of finite Clifford algebras, 1. Classification, J. Math. Phys. 32 (1991) 1657.
6. R. D'Auria, S. Ferrara, M.A. Lledó and V.S. Varadarajan, Spinor algebras, J. Geom. Phys. 40 (2001) 101 [hep-th/0010124];
7. R. D'Auria, S. Ferrara and M.A. Lledó, On the embedding of space-time symmetries into simple superalgebras, Lett. Math. Phys. 57 (2001) 123 [hep-th/0102060];
8. S. Ferrara and M.A. Lledó, Considerations on superpoincare algebras and their extensions to simple superalgebras, Rev. Mod. Phys. 14 (2002) 519 [hep-th/0112177].
9. R. Haag, J.T. Lopuszański and M. Sohnius, All possible generators of supersymmetries of the S matrix, Nucl. Phys. B 88 (1975) 257.
10. J. Lukierski and F. Toppan, Generalized space-time supersymmetries, division algebras and octonionic M-theory, Phys. Lett. B 539 (2002) 266 [hep-th/0203149].
11. J. Lukierski and F. Toppan, Octonionic M-theory and D = 11 generalized conformal and superconformal algebras, hep-th/0212201.
12. P. Jordan, Über eine Klasse nichtassociativer hypercomplexer Algebren, Nachr. Ges. Wiss. Gött. Math. Phys. 569 (1932);
13. Nachr. Ges. Wiss. Gott. Math. Phys. 209 (1933);
14. Zeits. Phys. 80 (1933) 285;
15. P. Jordan, J. von Neumann and E.P. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. Math. 35 (1934) 29.
16. D.B. Fairlie and C.A. Manogue, Lorentz invariance and the composite string, Phys. Rev. D 34 (1986) 1832.
17. K.W. Chung and A. Sudbery, Octonions and the Lorentz and conformal groups of ten-dimensional space-time, Phys. Lett. B 198 (1987) 161.
18. S. Okubo, Real representations of Clifford algebras, II. Explicit construction and pseudo-octonion, J. Math. Phys. 32 (1991) 1669.
19. J. Lukierski and P. Minnaert, Seven spheres from octonions and geometric torsion, Phys. Lett. B 129 (1983) 392;
20. Z. Hasiewicz and J. Lukierski, Supersymmetrized D = 11 de Sitter like algebra from octonions, Phys. Lett. B 145 (1984) 65.
21. M. Cederwall and C.R. Preitschopf, S7 and S7 (Kac-Moody algebra), Commun. Math. Phys. 167 (1995) 373 [hep-th/9309030].
22. M.A. De Andrade and F. Toppan, Real structures in Clifford algebras and majorana conditions in any space-time, Mod. Phys. Lett. A 14 (1999) 1797 [hep-th/9904134].
23. L. Smolin, The exceptional Jordan algebra and the matrix string, hep-th/0104050.
24. C.A. Barton and A. Sudbery, Magic squares and matrix models of Lie algebras, math.RA/0203010.
25. P. Ramond, Algebraic dreams, hep-th/0112261.
26. 6 matrix model, Prog. Theor. Phys. 108 (2002) 755 [hep-th/0110106].
27. L.J. Boya, Octonions and M-theory, hep-th/0301037.
28. J. Baez, The octonions, math.RA/0105155.
29. M. Günaydin and S.V. Ketov, Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras, Nucl. Phys. B 467 (1996) 215 [hep-th/9601072].
30. E. Bergshoeff, E. Sezgin, P, Townsend, Properties of the eleven-dimensional super membrane theory, Ann. Phys. (NY) 185 (1988) 330.
31. M.J. Duff, R.R. Khuri and J.X. Lu, String solitons, Phys. Rept. 259 (1995) 213 [hep-th/9412184].
32. F. Toppan, Division algebras, extended supersymmetries and applications, Nucl. Phys. 102 (Proc. Suppl.) (2001) 270 [hep-th/0109073].
33. H.L. Carrion, M. Rojas and F. Toppan, Octonionic realizations of 1-dimensional extended supersymmetries. a classification, Mod. Phys. Lett. A 18 (2003) 787 [hep-th/0212030].
34. M.J. Duff, B.E.W. Nilsson and C.N. Pope, Kaluza-Klein supergravity, Phys. Rept. 130 (1986) 1.
35. M. Günaydin, C. Piron and H. Ruegg, Moufang plane and octonionic quantum mechanics, Commun. Math. Phys. 61 (1978) 69.