What question did this study set out to answer?

The research aims to introduce and classify root systems extended by an abelian group G, focusing on their properties and applications.

March 29, 2026Journal of Lie theoryOpen Access

Root Systems Extended by an Abelian Group and their Lie Algebras

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Classifies root systems extended by an abelian group, highlighting implications for graded Lie algebras.

The research aims to introduce and classify root systems extended by an abelian group G, focusing on their properties and applications.
Introduced the concept of root systems extended by an abelian group G
Classified these root systems using translated reflection spaces of G
Examined division (G)-graded Lie algebras that contain these root systems
Classified division (B l , G)-graded Lie algebras for l ≥ 3
Provided a classification of root systems extended by an abelian group G
Established connections to graded Lie algebras and reflection spaces
Classified Lie G-tori of type B l for l ≥ 3

Y. Yoshii (2004) studied this question.

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