Parabolic sets of roots

2009/04/01 by Ivan Dimitrov, Vyacheslav Futorny, Dimitrov, Ivan +3
Mathematics · #17B20 #17B65 #17B67 #FOS: Mathematics #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:17B20 #msc:17B65 #msc:17B67

paper · pdf · doi:10.48550/arxiv.0904.0041

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openalex publication_date 2009/04/01 · arxiv created 2009/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compare two combinatorial definitions of parabolic sets of roots. We show that these definitions are equivalent for simple finite dimensional Lie algebras, affine Lie algebras, and toroidal Lie algebras. In contrast, these definitions are not always equivalent for simple finite dimensional Lie superalgebras.

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