Browse > Article

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

Kim, Yeon-Ok (DEPARTMENT OF MATHEMATICS, SOONGSIL UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.17, no.1, 2010 , pp. 107-113 More about this Journal
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 ($k\;{\in}\;\mathbb{Z}$>0). We also give several relations between the roots on g(A).
Keywords
generalized Cartan matrix; Kac-Moody algebra; hyperbolic type;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Y. Kim, K.C. Misra & S.J. Stizinger: On the degree of nilpotency of certain subalgebras of Kac-Moody Lie algebras. J. Lie Theory 14 (2004), 11-23
2 R.V. Moody: Root System of Hyperbolic Type. Adv. in Math. 33 (1979) 144-160.   DOI
3 R.V. Moody: A new class of Lie algebras. J. Algebra 10 (1968), 210-230.
4 S.-J, Kang: Root multiplicities of Kac-Moody Algrbras ${H_n}^{(1)$. J. Algebra 170 (1994), 277-299.   DOI   ScienceOn
5 S.-J, Kang & D.J. Melville: Rank 2 Symmetric Hyperbolic Kac-Moody Algebras. Nagoya. Math. J. 140 (1995), 41-75.   DOI
6 A.J. Feingold: A hyperbolic GCM and the Fibonachi numbers. Proc. Amer. Math. Soc. 80 (1980), 379-385.   DOI   ScienceOn
7 G.M, Benkart, S.-J, Kang & K.C. Misra: Graded Lie Algebras of Kac-Moody Type. Adv. in Math. 97 (1993), 154-190.   DOI   ScienceOn
8 V.G. Kac: Infinite-Dimensional Lie Algebras. Cambridge University Press, 1990.