Higher-order simple Lie algebras

Communications in Mathematical Physics

Volumn 184, Issue 3, 1997, Pages 669-681

  De Azcarraga J A ^a,b,c   Perez Bueno J C ^a,b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b INSTITUTO DE FÍSICA CORPUSCULAR IFIC   (Spain)

^c UNIVERSITY OF VALENCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039768859     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050079     Document Type: Article

References (44)

1. Cartan, E.: La topologie des groupes de Lie. L'Enseignement math. 35, 177-200 (1936)
2. Pontrjagin, L.: Sur les nombres de Betti des groupes de Lie. C. R. Acad. Sci. Paris 200, 1277-1280 (1935)
3. Hopf, H.: Über die topologie der gruppen-manigfaltigkeiten und ihre Verallgemeinerungen. Ann. Math. 42, 22-52 (1941)
4. Hodge, W. V. D.: The theory and applications of harmonic integrals. Camb. Univ. Press (1941)
5. Chevalley, C. and Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. Trans. Am. Math. Soc. 63, 85-124 (1948)
6. Samelson, H.: Topology of Lie groups. Bull. Am. Math. Soc. 57, 2-37 (1952)
7. Borel, A. and Chevalley C.: The Betti numbers of exceptional groups. Mem. Am. Math. Soc. 14, 1-10 (1955)
8. Borel, A.: Topology of Lie groups and characteristic classes. Bull. Am. Math. Soc. 61, 397-432 (1965)
9. Bott, R.: The geometry and representation theory of compact Lie groups. in London Math. Soc. Lecture Notes Ser. 34, 65-90, Camb. Univ. Press (1979)
10. Racah, G.: Sulla caratterizzazione delle rappresentazioni irreducibili dei gruppi semisimplici di Lie. Lincei-Rend. Sc. fis. mat. e nat. VIII, 108-112 (1950); Princeton lectures, CERN-61-8 (reprinted in Ergeb. Exact Naturwiss. 37, 28-84 (1965)), Springer-Verlag
11. Racah, G.: Sulla caratterizzazione delle rappresentazioni irreducibili dei gruppi semisimplici di Lie. Lincei-Rend. Sc. fis. mat. e nat. VIII, 108-112 (1950); Princeton lectures, CERN-61-8 (reprinted in Ergeb. Exact Naturwiss. 37, 28-84 (1965)), Springer-Verlag
12. Biedenharn, L. C.: On the representations of the semisimple Lie groups I. J. Math. Phys. 4, 436-445 (1963)
13. Klein, A.: Invariant operators of the unimodular group in n dimensions. J. Math. Phys. 4, 1283-1284 (1963)
14. Gruber, B. and Raifeartaigh, O.: S-theorem and construction of the invariants of the semisimple compact Lie algebras. J. Math. Phys. 5, 1796-1804 (1964)
15. Perelomov, A. M. and Popov, V. S.: Casimir operators for semisimple groups. Math. USSR-Izvestija 2, 1313-1335 (1968)
16. Nwachuku, C. O. and Rashid, M. A.: Eigenvalues of the Casimir operators of the orthogonal and symplectic groups. J. Math. Phys. 17, 1611-1616 (1976)
17. Okubo, S. and Patera, J.: General indices of representations and Casimir invariants. J. Math. Phys. 25, 219-227 (1983)
18. Okubo, S.: Modified fourth-order Casimir invariants and indices for simple Lie algebras. J. Math. Phys. 23, 8-20 (1982)
19. For an outlook including further references, see the articles by Jackiw and Zumino in Treiman. S. B.; Jackiw, R.; Zumino, B. and Willen, E.: Current algebra and anomalies World Sci. (1985)
20. Atiyah, M. F. and Jones, J. D. S.: Topological aspects of Yang-Mills theory. Commun. Math. Phys. 61, 97-118 (1978)
21. Kephart, T. W.: Safe groups and anomaly cancellation in even dimensions. Phys. Lett. B151, 267-270 (1985)
22. Okubo, S. and Patera, J.: Cancellation of higher order anomalies. Phys. Rev. D31, 2669-2671 (1985)
23. Lada, T. and Stasheff, J.: Introduction to SH Lie algebras for physicists. Int. J. Theor. Phys. 32, 1087-1103 (1993)
24. Lada, T. and Markl, M.: Strongly homotopy Lie algebras. Commun. in Alg. 23, 2147-2161 (1995)
25. Witten, E. and Zwiebach, B.: Algebraic structures and differential geometry in two-dimensional string theory. Nucl. Phys. B377, 55-112 (1992)
26. Zwiebach, B.: Closed string theory: quantum action and the Batalin-Vilkovisky master equation. Nucl. Phys. B390, 33-152 (1993)
27. de Azcárraga, J. A., Perelomov, A. M. and Pérez Bueno, J. C.: New Generalized Poisson Structures. J. Phys. A29, L151-L157 (1996); The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures. J. Phys. A29 7993-8009 (1996)
28. de Azcárraga, J. A., Perelomov, A. M. and Pérez Bueno, J. C.: New Generalized Poisson Structures. J. Phys. A29, L151-L157 (1996); The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures. J. Phys. A29 7993-8009 (1996)
29. Jones, E. S.: A study of Lie and associative algebras from a homotopy point of view. Master's project. North Carolina Univ., Raleigh (1990)
30. Hanlon, P. and Wachs, H.: On Lie k-algebras. Adv. in Math. 113, 206-236 (1995)
31. Weyl, H.: The classical groups. Princeton (1946)
32. Englefield, M. and King, R. C.: Symmetric power sum expansions of the eigenvalues of generalised Casimir operators of semi-simple Lie groups. J. Phys. A13, 2297-2317 (1980)
33. Boya, L. J.: Representations of simple Lie groups. Rep. Math. Phys. 32, 351-354 (1993)
34. Sudbery, A.: Computer-friendly d-tensor identities for SU(n). J. Phys. A23(15), L705-L710 (1990)
35. 8. ibid. 1857-1860
36. 8. ibid. 1857-1860
37. de Azcárraga, J. A. and Townsend, P. K.: Superspace geometry and classification of supersymmetric extended objects. Phys. Rev. Lett. 62, 2579-2512 (1989)
38. Lian, B.H. and Zuckerman, G.J.: New perspectives on the BRST-algebraic structure of string theory. Commun. Math. Phys. 154, 613-646 (1993)
39. Henneaux, M.: The antifield BRST formalism. Nucl. Phys. B (Proc. Suppl.) 18A, 47-106 (1990)
40. Gomis, J.; Paris, J. and Samuel, S.: Antibracket, antifields and gauge-theory quantization. Phys. Rep. 259, 1-145 (1995)
41. Bering, K.; Damgaard, P. H. and Alfaro, J.: Algebra of higher antibrackets. Nucl. Phys. B478, 459-503 (1996)
42. Gel'fand. I.M.: The Center of an infinitesimal groupring. Mat. Sbornik 26, 103-112 (1950) (English trans. by Los Alamos Sci, Lab. AEC-TR-&6133 (1963))
43. Abellanas, L. and Martínez Alonso, L.: A general setting for Casimir invariants. J. Math. Phys. 16, 1580-1584 (1975)
44. Bais, F. A., Bouwnegt, P., Surridge, M. and Schoutens, K.: Extensions of the Virasoro algebra constructed from KAC-Moody algebras using higher order Casimir invariants. Nucl. Phys. B304, 348-370 (1988)