Extended Affine Root System IV (Simply-Laced Elliptic Lie Algebras)

Publications of the Research Institute for Mathematical Sciences

Volumn 36, Issue 3, 2000, Pages 385-421

  Saito, Kyoji ^a   Yoshii, Daigo ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85015588690     PISSN: 00345318     EISSN: None     Source Type: Journal    
DOI: 10.2977/prims/1195142952     Document Type: Article

References (48)

1. Allison, Bruce N., Azam, Saeid, Berman, Stephan, Gao, Yuri and Pianzola, Ar-turo, Extended Affine Lie Algebras and their Root systems, Mem. Amer. Math. Soc., 126 (1997).
2. Azam, Saed, Construction of extended affine Lie algebras by the twisting process, Preprint, (1998).
3. Bourbaki, N., Lie alg. chap.3,4 et 5, Hermann, Paris, 1968.
4. Berman, Stephen and Billig, Yuly, Irreducible Representations for Toroidal Lie Algebras, Preprint, (1998).
5. Berman, Stephen, Gao, Y. and Krylyuk, Y., Quantum tori and the structure of elliptic quasi-simple Lie algebras, J. Fund. Anal., 135 (1996), 339–389.
6. Berman, Stephen, Jurisich, Elizabeth and Tan, Shaobin, Beyond Borcherds Lie Algebras and Inside, Preprint, (1998).
7. Berman, Stephen and Moody, R. V., Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy, Invent. Math., 108 (1992), 323–347.
8. Borcherds, Richard, Vertex algebras, Kac-Moody algebras and the Monster, Proc. Nat. Acad. Sci. USA, 83 (1986), 3068–3071.
9. Borcherds, Richard, Monstrous moonshine and monstrous Lie superalgebras, Invent. Math., 109 (1992), 405–444.
10. Borcherds, Richard, Generalized Kac-Moody algebras, J. Algebra, 115 (1988), 501–512.
11. Eswara Rao, S. and Moody, R. V., Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebra, Comm. Math. Phys., 159 (1994), 239–264.
12. Frenkel, Igor, B., Representations of Kac-Moody Algebras and Dual Resonance Models, Lectures in Appl. Math., 21 (1985), 325–353.
13. Frenkel, Igor B and Kac, Victor, Basic Representations of Affine Lie Algebras and Dual Resonance Models, Invent. Math., 62 (1980), 23–66.
14. Frenkel, Igor, B., Lepowsky and Meurman, Vertex operator algebras and the Monster, Academic Press, 1988.
15. Gebert, R. W., Introduction to vertex algebras, Borcherds algebras, and the monster Lie algebra, Internat. J. Modern Phys. A, 8 (1993), 5441–5503.
16. Gebert, R. W. and Nicolai, H., On Eio and the DDF construction, Comm. Math. Phys., 172 (1995), 571–622.
17. Iohara, Kenji, Saito, Yoshihisa and Wakimoto, Minoru, Hirota Bilinear Forms with 2-Toroidal Symmetry, Phys. Lett. A, 254 (1999), 37–46.
18. Kac, Victor, Infinite Dimensional Lie Algebras, Birkhauser (third edition).
19. Kac, Victor, Vertex Algebras for Beginners, Univ. Lecture Ser., 10 (1998).
20. Kassel, C., Kaehler Differentials and coverings of complex simple Lie algebras extended over a commutative ring, J. Pure Appl. Algebra, 34 (1984), 265–275.
21. Macdonald, I.G. Ivan, Affine root Systems and Dedekind's 77-Function, Invent. Math., 15 (1972), 91–143.
22. Moody, R. V., Eswara Rao, S. and Yokonuma, T., Toroidal Lie algebras and vertex representation, Geom. Dedicata, 35 (1990), 283–307.
23. Matsuo, Atsushi and Nagatomo, Kiyokazu, Axioms for a vertex algebra and the locality of quantum fields, MS J Memoirs, 4 (1999).
24. Moody, R. V. and Pianzola, A., Lie algebras with triangular decomposition, John Wiley, New York, 1995.
25. Pollmann, Ulrike, Realization der biaffinen Wurzelsystem von Saito in Lie-Algebren, Hamburger Beitrage zur Mathematik, Heft, 29 (1994).
26. Pressley, A. and Segal, G., Loop groups, Oxford: Oxford University Press, 1986.
27. Saito, Kyoji, Einfach Elliptische Singularitaten, Invent. Math., 23 (1974), 289–325.
28. Saito, Kyoji, Period mapping associated to a primitive form, Publ. RIMS, Kyoto Univ., 19 (1983), 1231–1264.
29. Saito, Kyoji, Extended Affine Root systems, I., (Coxeter Transformations), Publ. RIMS, Kyoto Univ., 21 (1985), 75–179.
30. Saito, Kyoji, Extended Affine Root systems II (Flat Invariants), Publ. RIMS, Kyoto Univ., 26 (1990), 15–78.
31. Saito, Kyoji and Takebayashi, T., Extended Affine Root systems III (Elliptic Weyl Groups), Publ. RIMS, Kyoto Univ., 33 (1997), 301–329.
32. Saito, Kyoji, Extended Affine Root systems III (Elliptic eta-product and Elliptic L-function), Preprint, (1998).
33. Saito, Kyoji, Around the Theory of the Generalized Weight System: Relations with Singularity Theory, the Generalized Weyl Group and Its Invariant Theory, Etc., Amer. Math. Soc. Transl. Ser 2, 183 (1998), 101–143.
34. Sasaki, Shoichi, Master thesis, Saitama University, 1996.
35. Satake, Ikuo, Automorphism of the Extended Affine Root System and Modular Property for the Flat Theta Invariants, Publ. RIMS, Kyoto Univ., 31 (1995), 1–32.
36. Satake, Ikuo, Flat Structure for the simple Elliptic Singularities of type E6, Proc. Japan Acad. Ser. A, 69 (1993), 247–251.
37. Satake, Ikuo, Flat Theta Invariants and Jacobi form of type D4, Proceedings of 31th Tamguchi Symposium, Birkhauser (1998).
38. Serre, Jean Pierre, Algebres de Lie semi-simple complexes, Benjamin, New York and Amsterdam, 1966.
39. Slodowy, Peter, Simple singularities and simple algebraic group, Lecture Notes in Math., 815 (1980)
40. Slodowy, Peter, Smgularitaeten, Kac-Moody-Lie algebren, assozierte Gruppen und Verallgemeinerungen, Habilitationsschrift, 1984.
41. Slodowy, Peter, Another new class of Lie algebras, 1984.
42. Slodowy, Peter, Beyond Kac-Moody algebras and inside, Can. Math. Soc. Proc, 5 (1986), 361–371.
43. Van der Lek, H., Extended Artin Groups, Proc. Sympos. Pure Math., 40, Part 2 (1983), 117–122.
44. Wakimoto, Minoru, Extended Affine Lie Algebras and a Certain Series of Hermitian Representations, Department of Mathematics, Faculty of Science, Hiroshima University, 1985.
45. Yamada, Hiroshi, Extended affine Lie Algebras and their Vertex representations, Publ. RIMS, Kyoto Univ., 25 (1989), 587–603.
46. Yamada, Hiroshi, Lie group theoretical construction of period mapping, Math. Z., 220(1995), 231–255.
47. Yamada, Hiroshi, Elliptic Root Systems and Elliptic Artin Group, Preprint, (1998).
48. Yoshii, Daigo, Elliptic Lie algebra of type E8(1,1), Master thesis, 1997.