The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A NOTE ON THE RANK 2 SYMMETRIC HYPERBOLIC KAC-MOODY ALGEBRAS

  • Kim, Yeon-Ok (DEPARTMENT OF MATHEMATICS, SOONGSIL UNIVERSITY)
  • Published : 2010.02.28
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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

References

  1. G.M, Benkart, S.-J, Kang & K.C. Misra: Graded Lie Algebras of Kac-Moody Type. Adv. in Math. 97 (1993), 154-190. https://doi.org/10.1006/aima.1993.1005
  2. A.J. Feingold: A hyperbolic GCM and the Fibonachi numbers. Proc. Amer. Math. Soc. 80 (1980), 379-385. https://doi.org/10.1090/S0002-9939-1980-0580988-6
  3. V.G. Kac: Infinite-Dimensional Lie Algebras. Cambridge University Press, 1990.
  4. S.-J, Kang: Root multiplicities of Kac-Moody Algrbras ${H_n}^{(1)$. J. Algebra 170 (1994), 277-299. https://doi.org/10.1006/jabr.1994.1338
  5. S.-J, Kang & D.J. Melville: Rank 2 Symmetric Hyperbolic Kac-Moody Algebras. Nagoya. Math. J. 140 (1995), 41-75. https://doi.org/10.1017/S0027763000005419
  6. 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
  7. R.V. Moody: Root System of Hyperbolic Type. Adv. in Math. 33 (1979) 144-160. https://doi.org/10.1016/S0001-8708(79)80003-1
  8. R.V. Moody: A new class of Lie algebras. J. Algebra 10 (1968), 210-230.