What question did this study set out to answer?

The aim is to establish conditions under which indefinite Kac-Moody algebras can have a minimal Z-gradation.

March 29, 2026Open Access

Local Lie Algebras and some Kac-Moody Algebras of Indefinite Type

Key Points

The aim is to establish conditions under which indefinite Kac-Moody algebras can have a minimal Z-gradation.
Demonstrated conditions for minimal Z-gradation
Explored examples of orbit Lie algebras from 2-fold affinization
Discussed properties of Lorentzian Kac-Moody algebras
Identified a sufficient condition for the existence of minimal Z-gradation
Provided examples illustrating applications of identified orbit Lie algebras
Showed the integration of local parts using highest weight modules

Abstract

We show a sufficient condition for an indefinite Kac-Moody algebra to admit minimal Z-gradation with local part given by an integrable highest weight module.Examples of orbit Lie algebras arising from 2-fold affinization and Lorentzian Kac-Moody algebras are discussed.

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