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  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 32, Issue 2, Pages 243 - 254 (August 2008)


DEFINING RELATIONS OF THE SIMPLY-LACED 4-EXTENDED AFFINE LIE ALGEBRAS

Tadayoshi Takebayashi (Japan)

Received March 27, 2008

References:



[1] S. Berman and R. V. Moody, Lie algebras graded by finite root systems and the intersection matrix algebras of Sodowy, Invent. Math. 108 (1992), 323-347.

[2] R. Borcherds, Vertex algebras, Kac-Moody algebras and the Monster, Proc. Nat. Acad. Sci. USA 83 (1986), 3068-3071.

[3] R. V. Moody, S. Eswara Rao and T. Yokonuma, Toroidal Lie algebra and vertex representation, Geom. Dedicata 35 (1990), 283-307.

[4] S. Eswara Rao and R. V. Moody, Vertex representations for n-toroidal Lie algebra and a generalization of the Virasoro algebra, Commun. Math. Phys. 159 (1994), 239-264.

[5] K. Saito, Extended affine root systems I (Coxeter transformations), Publ. RIMS, Kyoto Univ. 21 (1985), 75-179.

[6] K. Saito and D. Yoshii, Extended affine root systems IV (Simply-laced elliptic Lie algebras), Publ. RIMS, Kyoto Univ. 36 (2000), 385-421.

[7] P. Slodowy, Beyond Kac-Moody algebras and inside, Can. Math. Soc. Proc. 5 (1986), 361-371.

[8] T. Takebayashi, On the defining relations of the simply-laced elliptic Lie algebras, Proc. Japan Acad. Ser. A 77 (2001), 119-121.

[9] T. Takebayashi, Note on the defining relations of the elliptic Lie algebras with rank JP J. Algebra, Number Theory and Appl. 8(1) (2007), 1-4.

[10] T. Takebayashi, Defining relations of the simply-laced 3-extended affine Lie algebras, JP J. Algebra, Number Theory and Appl. 8(1) (2007), 45-68.

[11] T. Takebayashi, Defining relations of the non simply-laced 3-extended affine Lie algebras of type Far East J. Appl. Math. 28(2) (2007), 183-208.

[12] Hiroyuki Yamane, A Serre-type theorem for the elliptic Lie algebras with rank Publ. RIMS, Kyoto Univ. 40 (2004), 441-469.

Keywords and phrases: 4-extended affine Lie algebra, simply-laced.

 


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