Abstract
In this work, we develop a homological theory for the graded Lie algebras, which gives new information on the structure of the Lorentzian Kac-Moody Lie algebras. The technique of the Hochschild-Serre spectral sequences offers a uniform method of studying the higher level root multiplicities and the principally specialized affine characters of Lorentzian Kac-Moody Lie algebras.
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