The root system and the core of an extended affine Lie algebra

Selecta Mathematica, New Series

Volumn 7, Issue 2, 2001, Pages 149-212

  Allison, Bruce N ^a   Gao, Yun ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b YORK UNIVERSITY   (Canada)

Author keywords

Infinite dimensional Lie algebra; Jordan algebra; Nonassociative algebra; Root system

Indexed keywords

EID: 0002227093     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/PL00001400     Document Type: Article

References (29)

1. [AABGP] B.N. Allison, S. Azam, S. Berman, Y. Gao and A. Pianzola. Extended affine Lie algebras and their root systems. Memoir Amer. Math. Soc. 126 (1997), no. 603, 1-122.
2. [BZ] G. M. Benkart and E. I. Zelmanov. Lie algebras graded by finite root systems and intersection matrix algebras. Invent. Math. 126 (1996), 1-45.
3. [BGK] S. Berman, Y. Gao and Y. Krylyuk. Quantum tori and the structure of elliptic quasi-simple Lie algebras. J. Fund. Anal 135 (1996), 339-389.
4. 2. Trans. Amer. Math. Soc 347 (1995), 4315-4363.
5. [BM] S. Berman and R. V. Moody. Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Invent. Math 108 (1992), 323-347.
6. 2 with coordinates in a simple quantum torus with two variables. Recent developments in quantum affine algebras and related topics, Contemp. Math., vol. 248. Amer. Math. Soc., Providence, RI, 1999, 39-67.
7. [Di] J. Dieudonné. La géométrie des groupes classiques. Troisiéme Edition. Springer-Verlag, New York, 1971.
8. [F] J. R. Faulkner. Barbilian planes. Geom. Dedicata 30 (1989), 125-181.
9. [G1] Y. Gao. The degeneracy of extended affine Lie algebras. Manuscripta Math 97 (1998), 233-249.
10. [G2] Y. Gao. Representations of extended affine Lie algebras coordinatized by certain quantum tori. Composite Mathematica 123 (2000), 1-25.
11. N. Comm. Math. Phys. 211 (2000), 745-777.
12. [H] J.E. Humphreys. Introduction to Lie Algebras and Representation Theory. Springer-Verlag, New York, 1972.
13. [HT] R. Høegh-Krohn and B. Torresani. Classification and construction of quasi-simple Lie algebras. J. Fund. Anal. 89 (1990), 106-136.
14. [J1] N. Jacobson. Structure and representations of Jordan algebras. Amer. Math. Soc. Colloq. Publ., vol. 39. Amer. Math. Soc., Providence, R.I., 1968.
15. [J2] N. Jacobson. Exceptional Lie Algebras. Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York, 1971.
16. [M] Y. I. Manin. Topics in Noncommutative Geometry. Princeton University Press, 1991.
17. [Mc] K. McCrimmon. A taste of Jordan algebras, preliminary version of a textbook on Jordan algebras.
18. [McN] K. McCrimmon and E. Neher. Coordinatization of triangulated Jordan systems. J. of Algebra 114 (1988), 411-451.
19. [MRY] R. V. Moody, S. E. Rao and T. Yokonuma. Toroidal Lie algebras and vertex representations. Geom. Ded. 35 (1990), 283-307.
20. [N] E. Neher. Lie algebras graded by 3-graded root systems. Amer. J. Math. 118 (1996), 439-491.
21. [Sa1] K. Saito. Extended affine root systems 1 (Coxeter transformations). Publ. RIMS., Kyoto Univ. 21 (1985), 75-179.
22. [Sa2] K. Saito. Extended Affine Root Systems 2 (flat invariants). Publ. RIMS., Kyoto Univ. 26 (1990), 15-78.
23. [Se] G. B. Seligman. Rational Methods in Lie Algebras. Lect. Notes Pure Appl. Math.. New York: M. Dekker, 1976.
24. [T] J. Tits. Une classe d'algèbres de Lie en relation avec les algèbres de Jordan. Indag. Math. 24 (1962), 530-535.
25. [Ya] H. Yamada. Extended affine Lie algebras and their vertex representations. Publ. RIMS, Kyoto U. 25 (1989), 587-603.
26. 1. University of Ottawa PhD thesis, 1999.
27. [Y2] Y. Yoshii. Jordan tori. C.R. Math. Rep. Acad. Sci. Canada 18 (1996), 153-158.
28. 1. J. of Algebra 234 (2000), 128-168.
29. [ZSSS] K.A. Zhevlakov, A.M. Slinko, J.P. Shestakov and A.I. Shirshov. Rings that are Nearly Associative. Academic Press, New York, 1982.