논문KCI 등재
A NOTE ON THE RANK 2 SYMMETRIC HYPERBOLIC KAC-MOODY ALGEBRAS
한국수학교육학회|2010.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제17권 제1호|pp. 107-113
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In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the suffcient conditions for existence of imaginary roots of square length -2k(k ∈ Z>0 ). We also give several relations between the roots on g(A).
Abstract
In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the suffcient conditions for existence of imaginary roots of square length -2k(k ∈ Z>0 ). We also give several relations between the roots on g(A).
참고문헌 (8)
- G.M, Benkart, "Graded Lie Algebras of Kac-Moody Type", Adv. in Math, 97, pp.154~190 (1993)
- A.J. Feingold, "A hyperbolic GCM and the Fibonachi numbers", Proc. Amer. Math. Soc, 80, pp.379~385 (1980)
- V.G. Kac, "Infinite-Dimensional Lie Algebras" (1990), Cambridge University Press
- S.-J, Kang, "Root multiplicities of Kac-Moody Algrbras HA(1)n", J. Algebra, 170, pp.277~299 (1994)
- S.-J, Kang, "Rank 2 Symmetric Hyperbolic Kac-Moody Algebras", Nagoya. Math. J, 140, pp.41~75 (1995)
- Y. Kim, "On the degree of nilpotency of certain subalgebras of Kac-Moody Lie algebras", J. Lie Theory, 14, pp.11~23 (2004)
- R.V. Moody, "Root System of Hyperbolic Type", Adv. in Math, 33, pp.144~160 (1979)
- R.V. Moody, "A new class of Lie algebras", J. Algebra, 10, pp.210~230 (1968)
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