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Finite Dimensional Simple Modules over Some GIM Lie Algebras

Author

Listed:
  • Limeng Xia

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, China
    These authors contributed equally to this work.)

  • Dong Liu

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
    Department of Mathematics, Huzhou University, Huzhou 313000, China
    These authors contributed equally to this work.)

Abstract

GIM Lie algebras are the generalizations of Kac–Moody Lie algebras. However, the structures of GIM Lie algebras are more complex than the latter, so they have encountered many new difficulties to study their representation theory. In this paper, we classify all finite dimensional simple modules over the GIM Lie algebra Q n + 1 ( 2 , 1 ) as well as those over Θ 2 n + 1 .

Suggested Citation

  • Limeng Xia & Dong Liu, 2022. "Finite Dimensional Simple Modules over Some GIM Lie Algebras," Mathematics, MDPI, vol. 10(15), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2658-:d:874448
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