Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras

Limeng XIA; Hongmei HU; Yilan TAN

doi:10.1007/s11464-022-0072-8

Frontiers of Mathematics ›› 2024, Vol. 19 ›› Issue (1) :161 -170. DOI: 10.1007/s11464-022-0072-8

RESEARCH ARTICLE

Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras

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Abstract

In this paper, we study the finite dimensional modules over indefinite Kac–Moody Lie algebras. We prove that any Kac–Moody Lie algebra with indecomposable indefinite Cartan matrix has no non-trivial finite dimensional simple module. This result would be indispensable for researching finite dimensional modules over GIM Lie algebras.

Keywords

Indefinite type / hyperbolic / Kac–Moody algebra / finite dimensional module

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Limeng XIA, Hongmei HU, Yilan TAN. Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras. Frontiers of Mathematics, 2024, 19(1): 161-170 DOI:10.1007/s11464-022-0072-8