References
M. Atiyah,K-Theory, W.A. Benjamin, New York, 1967.
R. Borcherds, Generalized Kac-Moody Lie algebras,J. Algebra 115 (1988), 501–512.
R. Borcherds, Central extensions of generalized Kac-Moody Lie algebras,J. Algebra 140 (1991), 330–335.
R. Borcherds, Monstrous moonshine and monstrous Lie superalgebras,Invent. Math. 109 (1992), 405–444.
R. Borcherds, Sporadic groups and string theory, to appear.
N. Bourbaki,Lie Groups and Lie Algebras, Part 1, Hermann, Paris, 1975.
H. Cartan and S. Eilenberg,Homological Algebra, Princeton University Press, 1956.
J.H. Conway and S.P. Norton, Monstrous Moonshine,Bull. London Math. Soc. 11 (1979), 308–339.
C.J. Cummins and S.P. Norton, Rational Hauptmoduls are replicable, to appear.
C. Ferenbaugh, Replication formulae for Monster-like functions, to appear.
I. Frenkel, J. Lepowsky and A. Meurman, A natural representation of the Fischer-Griess Monster with the modular functionJ as character,Proc. Natl. Acad. Sci. USA 81 (1984), 3256–3260.
I. Frenkel, J. Lepowsky and A. Meurman,Vertex Operator Algebras and the Monster, Academic Press, Boston, 1988.
O. Gabber and V. Kac, On defining relations of certain infinite-dimensional Lie algebras,Bull. Amer. Math. Soc. 5 (1981), 185–189.
H. Garland and J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas,Invent. Math. 34 (1976), 37–76.
R. Gebert and J. Teschner, On the fundamental representation of Borcherds algebras with one imaginary simple root,Lett. Math. Phys, to appear.
P. Goddard and C. Thorn, Compatability of the dual Pomeron with unitarity and the absence of ghosts in the dual resonance model,Phys. Lett. 43 No. 2 (1972), 235–238.
K. Harada, M. Miyamoto and H. Yamada, A generalization of Kac-Moody Lie algebras, to appear.
E. Jurisich,Generalized Kac-Moody algebras and their relation to free Lie algebras, Ph.D. thesis, Rutgers University, May, 1994.
E. Jurisich, Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra,J. Pure and Applied Algebra, to appear.
V. Kac, Simple irreducible graded Lie algebras of finite growth,Math. USSR Izvestija 2 (1968), 1271–1311.
V. Kac,Infinite Dimensional Lie Algebras, Cambridge University Press, third edition, 1990.
S.-J. Kang, Generalized Kac-Moody Lie algebras and the modular functionj, Math. Ann. 298 (1994), 373–384.
D. Knutson, λ-Rings and the Representation Theory of the Symmetric Group, Lecture Notes in Mathematics308, Springer-Verlag, 1973.
M. Koike, On replication formula and Hecke operators, preprint.
J. Lepowsky,Lectures on Kac-Moody Lie algebras, Université Paris VI, 1978 (unpublished).
J. Lepowsky, Generalized Verma modules, loop space cohomology and Macdonald-type identities,Ann. Scient. Ec. Norm. Sup., 4 série12 (1979), 169–234.
R. Moody, A new class of Lie algebras,J. Algebra 10 (1968), 211–230.
S. Naito, The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras, I, The existence of the resolution,Publ. of the Research Institute for Mathematical Sciences 29 (1993), 709–730.
S.P. Norton, More on Moonshine, in:Computational Group Theory, Academic Press, London, 1984, 185–193.
J.-P. Serre,Lie Algebras and Lie Groups, W.A. Benjamin, New York, 1965.
J.-P. Serre,Algèbres de Lie semi-simples complexes, W.A. Benjamin, New York, 1966.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jurisich, E., Lepowsky, J. & Wilson, R.L. Realizations of the Monster Lie algebra. Selecta Mathematica, New Series 1, 129–161 (1995). https://doi.org/10.1007/BF01614075
Issue Date:
DOI: https://doi.org/10.1007/BF01614075