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ISSN : 1226-0657

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Vol.17 No.1

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A NOTE ON THE RANK 2 SYMMETRIC HYPERBOLIC KAC-MOODY ALGEBRAS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.1, pp.107-113
Kim, Yeon-Ok
Kim,, Y. (2010). A NOTE ON THE RANK 2 SYMMETRIC HYPERBOLIC KAC-MOODY ALGEBRAS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(1), 107-113.

Abstract

In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k (<TEX>$k\;{\in}\;\mathbb{Z}$</TEX>>0). We also give several relations between the roots on g(A).

keywords
generalized Cartan matrix, Kac-Moody algebra, hyperbolic type

Reference

1.

(2004). . J. Lie Theory, 14, 11-23.

2.

MOODY. (1979). . Advances in Mathematics, 33(2), 144-160. 10.1016/S0001-8708(79)80003-1.

3.

(1968). . J. Algebra, 10, 210-230.

4.

Kang, S.J.;Melville, D.J.. (1994). Root Multiplicities of the Kac-Moody Algebras HA<SUP>(1)</SUP><SUB>n</SUB>. Journal of Algebra, 170(1), 277-299. 10.1006/jabr.1994.1338.

5.

(1995). . Nagoya. Math. J., 140, 41-75.

6.

Benkart, G.;Kang, S.J.;Misra, K.C.. (1993). Graded Lie Algebras of Kac-Moody Type. Advances in Mathematics, 97(2), 154-190. 10.1006/aima.1993.1005.

7.

8.

Feingold, Alex Jay. (1980). A Hyperbolic GCM Lie Algebra and the Fibonacci Numbers. Proceedings of the American Mathematical Society, 80(3), 379-385. 10.1090/S0002-9939-1980-0580988-6.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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