On characteristic equations, trace identities and Casimir operators of simple Lie algebras

Journal of Mathematical Physics

Volumn 41, Issue 5, 2000, Pages 3192-3225

  Macfarlane, A J ^a   Pfeiffer, Hendryk ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347417     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533300     Document Type: Article

References (40)

1. A. J. Macfarlane, A. Sudbery, and P. H. Weisz, Commun. Math Phys. 11, 77 (1968).
2. J. A. de Azcárraga, A. J. Macfarlane, A. J. Mountain, and J. C. Pérez-Bueno, Nucl. Phys. B 510, 657 (1998).
3. K. Meyberg, Nova J. Alg. Geom. 2, 107 (1993).
4. A. Sudbery, Ph.D. thesis, Corpus Christi College, Cambridge, 1969.
5. A. Sudbery, J. Phys. A 23, L705 (1990).
6. M. A. Rashid and Saifuddin, J. Math. Phys. 14, 630 (1973).
7. G. Racah, Rend. Lincei, Ser. 8 VIII, 108 (1950).
8. I. M. Gel'fand, Math. Sb. 26, 103 (1950).
9. G. Racah, "Group theory and spectroscopy," Institute for Advanced Studies Lectures, 1951.
10. G. Racah, Ergebnisse der Exakten Naturwissenschaften (Springer-Verlag, Berlin, 1965), Vol. 37.
11. J. A. de Azcárraga and J. C Pérez-Bueno, Commun. Math. Phys. 184, 669 (1997).
12. J. A. de Azcárraga and J. M. Izquierdo, Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics (Cambridge University Press, Cambridge, 1995).
13. S. Okubo, J. Math. Phys. 18, 2382 (1977).
14. K. Meyberg, J. Alg. 84, 279 (1983).
15. P. Cvitanovič, Group Theory (Nordita Classics, Kobenhavn, 1984).
16. P. Cvitanovič, "Classical and exceptional Lie algebras as invariance algebras," Oxford University preprint 1977.
17. K. Meyberg, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1984, Vol. 54, p. 177.
18. A. J. Mountain. J. Math. Phys. 39, 5601 (1998).
19. M. D. Gould, J. Austr. Math. Soc. B 26, 257 (1985).
20. A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971).
21. H. S. Green, J. Math. Phys. 12, 2106 (1971).
22. R. Slansky, Phys. Rep. 79, 1 (1981).
23. J. Fuchs and C. Schweigert, Symmetries, Lie Algebras and Representations (Cambridge University Press, Cambridge, 1997).
24. S. Okubo, J. Math. Phys. 20, 586 (1979).
25. H. T. Wadzinski, Nuovo Cimento Soc. Ital. Fis., B 6, 247 (1969).
26. H. R. Karadayi and M. Gungormez, J. Math. Phys. 38, 5974 (1997); 38, 5991 (1997).
27. H. R. Karadayi and M. Gungormez, J. Math. Phys. 38, 5974 (1997); 38, 5991 (1997).
28. U. Lindstrom, M. Roček, and R. von Unge, Hyperkähler quotients and algebraic curves, hep-th/9908082.
29. L. M. Kaplan and M. Resnikoff, J. Math. Phys. 8, 2194 (1967).
30. S. Okubo, J. Math. Phys. 23, 8 (1982).
31. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, 3rd ed. (Springer-Verlag, New York, 1980).
32. V. S. Varadarajan, Lie groups, Lie algebras, and their Representations (Springer-Verlag, New York, 1984).
33. M. J. Englefield and R. King, J. Phys. A 13, 2297 (1980).
34. J. F. Cornwell, Group Theory in Physics (Academic, London, 1984), Vol. II.
35. F. Gürsey and C.-H. Tze, On the Role of Division, Jordan and Related Algebras in Particle Physics (World Scientific, Singapore, 1956).
36. R. E. Behrends, J. Dreitlein, C. Fronsdal, and B. W. Lee, Rev. Mod. Phys. 34, 1 (1962).
37. P. Ramond, Introduction to exceptional Lie groups and algebras, Caltech. preprint CALT-68-577, 1976.
38. S. Okubo, Introduction to Octonion and Other Non-associative Algebras in Physics (Cambridge University Press, Cambridge, 1995).
39. A. J. Macfarlane, to be published.
40. L. J. Boya, Rep. Math. Phys. 30, 149 (1991).