Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

REFLECTION OF ROOT LATTICES FOR GENERALIZED KAC-MOODY ALGEBRAS

  • Published : 2010.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we determine all elements in the root lattice of symmetrizable generalized Kac-Moody algebras whose reflections preserve the root systems. Also we discuss elements in the root lattices whose reflection preserve the root lattices.

Keywords

References

  1. C. Bennet, Imaginary roots of a Kac-Moody Lie algebra whose reflection preserve root multiplicities, J. Algebra 158(1993), 244-267. https://doi.org/10.1006/jabr.1993.1133
  2. Elizabeth Jurisich, An Expression of Generalized Kac-Moody algebras. Contemporary Mathmemathics Volume 194(1996).
  3. V. G. Kac, Infinite Dimensional Lie Algebra, 3rd ed., Cambridge, UK(1989).
  4. Zhao Kaiming, Reflection of Root Lattices for Kac-Moody Algebras, (1994).
  5. N. Sthanumoorthy and A. Uma Maheswari, Purely Imaginary Roots of Kac-Moody Algebras, Communication in Algebra, 24(2)(1996), 677-693. https://doi.org/10.1080/00927879608825591
  6. N. Sthanumoorthy and P. L. Lilly, Special Imaginary Roots of Generalized K ac-Moody Algebras, Communication in Algebra 30(2002), 4771-4787. https://doi.org/10.1081/AGB-120014666
  7. N. Sthanumoorthy and P. L. Lilly, A Note onPurely Imaginary Roots of Generalized Kac-Moody Algebras, Univ. of Madras, Chennai, India. Vol. 31(2003), 5467-5479.
  8. N. Sthanumoorthy and P. L. Lilly, Complete Classifications of Generalized Kac-Moody Algebras Possessing Special Imaginary Roots and Strictly Imaginary Property, Communication in Algebra, 35(2007), 2450-2471 . https://doi.org/10.1080/00927870701326106
  9. Z. Wan, Introduction to K ac-Moody Algebra, World Scientific Publishing Co. Pte. Ltd.(1991).