Atiyah, M.F.: K-theory. New York Amsterdam: Benjamin 1967 Google Scholar
Borcherds, R.E.: Vertex algebras, Kac-Moody algebras, and the monster. Proc. Natl. Acad. Sci. USA83, 3068–3071 (1986) Google Scholar
Borcherds, R.E.: Generalized Kac-Moody algebras. J. Algebra115, 501–512 (1988) Google Scholar
Borcherds, R.E.: Central extensions of generalized Kac-Moody algebras. J. Algebra140, 330–335 (1991) Google Scholar
Borcherds, R.E.: Lattices like the Leech lattice. J. Algebra130 (No. 1), 219–234 (1990) Google Scholar
Borcherds, R.E., Conway, J.H., Queen, L., Sloane, N.J.A.: A monster Lie algebra? Adv. Math.53, 75–79 (1984); this paper is reprinted as Chap. 30 of [12] Google Scholar
Cartan, H., Eilenberg, S.: Homological Algebra Princeton: Princeton University Press 1956 Google Scholar
Conway, J.H.: The automorphism group of the 26 dimensional even Lorentzian lattice. J. Algebra80, 159–163 (1983); this paper is reprinted as Chap. 27 of [12] Google Scholar
Conway, J.H., Sloane, N.J.A.: Sphere packings lattices and groups (Grundlehren de Math. Wiss., vol. 290) Berlin Heidelberg New York Springer 1988 Google Scholar
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of finite groups. Oxford: Clarendon Press 1985 Google Scholar
Frenkel, I.B.: Representations of Kac-Moody algebras and dual resonance models. In: Flato, et al. (eds.) Applications of group theory in theoretical physics. (Lect. Appl. Math., vol. 21, pp. 325–353) Providence, RI: Am. Math. Soc. 1985 Google Scholar
Frenkel, I.B., Lepowsky, J., Meurman, A.: Vertex operator algebras and the monster. Boston, MA Academic Press 1988 Google Scholar
Frenkel, I.B., Lepowsky, J., Meurman, A.: A natural representation of the Fischer-Griess monster with the modular function_J_ as character. Proc. Natl. Acad. Sci. USA81, 3256–3260 (1984) Google Scholar
Frenkel, I.B., Huang, Y-Z., Lepowsky, J.: On axiomatic formulations of vertex operator algebras and modules. (Preprint)
Frenkel, I.B., Garland, H., Zuckerman, G.: Semi-infinite cohomology and string theory. Proc. Natl. Acad. Sci. USA83, 8442–8446 (1986) Google Scholar
Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976) Google Scholar
Goddard, P., Thorn, C.B., Compatibility of the dual Pomeron with unitarity and the absence of ghosts in the dual resonance model, Phys. Lett. B40 (No. 2), 235–238 (1972) Google Scholar
Gunning, R.C.: Lectures on modular forms. (Ann. Math. Stud) Princeton: Princeton University Press 1962 Google Scholar
Kac, V.G.: Infinite dimensional Lie algebras, third ed. Cambridge: Cambridge University Press 1990; (the first and second editions (Basel: Birkhäuser 1983, and C.U.P. 1985) do not contain the material on generalized Kac-Moody algebras that we need.) Google Scholar
Koike, M.: On Replication Formula and Hecke Operators. Nagoya University (Preprint)
Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, 329–387 (1961) Google Scholar
Mahler, K.: On a class of non-linear functional equations connected with modular functions. J. Aust. Math. Soc.22A, 65–118 (1976) Google Scholar
Norton, S.P.: More on moonshine, Computational group theory, pp. 185–195. London: Academic Press 1984 Google Scholar
Norton, S.P.: Generalized Moonshine. (Proc. Symp. Pure Math., vol. 47 pp. 208–209) Providence, RI: Am. Math. Soc. 1987 Google Scholar
Serre, J.P.: A course in arithmetic. (Grad. Texts Math., vol. 7) Berlin Heidelberg New York: Springer 1973 Google Scholar
Thompson, J.G.: A finiteness theorem for subgroups of PSL(2,R) which are commensurable with PSL(2,Z). (Proc. Symp. Pure Math., vol. 37, pp. 533–555) Providence, RI: Am. Math. Soc. 1979 Google Scholar