Classification of finite simple Lie conformal superalgebras

Journal of Algebra

Volumn 258, Issue 1, 2002, Pages 23-59

  Fattori, Davide ^a   Kac, Victor G ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036961173     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00504-5     Document Type: Article

References (27)

1. A.B. Astashkevich, D.B. Fuchs, On the cohomology of the Lie superalgebra W(m, n), in: Unconventional Lie Algebras, in: Advances in Soviet Mathematics, Vol. 17, 1993, pp. 1-13.
2. F.A. Berezin, Automorphisms of a Grassman algebra, Math. Notes 1 (3) (1967) 180-184.
3. B. Bakalov, A. D'Andrea, V.G. Kac, Theory of finite pseudoalgebras, Adv. Math. 162 (2001) 1-140.
4. B. Bakalov, V.G. Kac, A.A. Voronov, Cohomology of conformal algebras, Commun. Math. Phys. 200 (1999) 561-598.
5. A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (2) (1984) 333-380.
6. R.J. Blattner, A theorem of Cartan and Guillemin, J. Differential Geom. 5 (1970) 295-305.
7. R.J. Blattner, Induced and produced representations of Lie algebras, Trans. Amer. Math. Soc. 144 (1969) 457-474.
8. R.E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Natl. Acad. Sci. USA 83 (1986) 3068-3071.
9. S.-J. Cheng, V.G. Kac, Conformal modules, Asian J. Math. 1 (1) (1997) 181-193; Erratum: Asian J. Math. 2 (1) (1998) 153-156.
10. S.-J. Cheng, V.G. Kac, A new N = 6 superconformal algebra, Commun. Math. Phys. 186 (1997) 219-231.
11. S.-J. Cheng, V.G. Kac, Structure of some ℤ-graded Lie superalgebras of vector fields, Transform. Groups 4 (2-3) (1999) 219-272.
12. A. D'Andrea, V.G. Kac, Structure theory of finite conformal algebras, Selecta Math. (N.S.) 4 (1998)377-418.
13. D.B. Fuchs, Cohomology of Infinite-Dimensional Lie Algebras, in: Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986.
14. V. Guillemin, A Jordan-Hölder decomposition for a certain class of infinite-dimensional Lie algebras, J. Differential Geom. 2 (1968) 313-345.
15. V. Guillemin, Infinite-dimensional primitive Lie algebras, J. Differential Geom. 4 (1970) 257-282.
16. V. Guillemin, S. Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc. 70 (1964) 16-47.
17. V.G. Kac, Infinite-dimensional Lie algebras, third edition, Cambridge University Press, Cambridge, 1990.
18. V.G. Kac, Vertex algebras for beginners, Univ. Lecture Ser., Vol. 10, AMS, Providence, RI, 1996, 2nd ed., 1998.
19. V.G. Kac, The idea of locality, in: H.-D. Doebner, et al. (Eds.), Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, World Scientific, Singapore, 1997, pp. 16-32, q-alg/9709008.
20. V.G. Kac, Lie superalgebras, Adv. Math. 26 (1977) 8-96.
21. V.G. Kac, Classification of infinite-dimensional simple linearly compact Lie superalgebras, Adv. Math. 139 (1998) 1-55.
22. V.G. Kac, Superconformal algebras and transitive group actions on quadrics, Commun. Math. Phys. 186 (1997) 233-252; Erratum: Commun. Math. Phys. 217 (2001) 697-698.
23. V.G. Kac, Classification of infinite-dimensional simple groups of supersymmetries and quantum field theory, GAFA, Geom. Funct. Anal., Special Volume GAFA2000, 162-183.
24. V.G. Kac, J.W. van de Leur, On classification of superconformal algebras, in: S.J. Gates, et al. (Eds.), Strings 88, World Scientific, Singapore, 1989, pp. 77-106.
25. A.L. Onishchik, E.B. Vinberg, Lie Groups and Algebraic Groups, Springer-Verlag, Berlin, 1990.
26. L.J. Santharoubane, The second cohomology group for Kac-Moody Lie algebras and Kähler differentials, J. of Algebra 125 (1989) 13-26.
27. M. Scheunert, The Theory of Lie Superalgebras. An Introduction, in: Lecture Notes in Math., Vol. 716, Springer-Verlag, Berlin, 1979.