1. On the structure of Kac–Moody algebras
- Author
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Timothée Marquis and UCL - SST/IRMP - Institut de recherche en mathématique et physique
- Subjects
Nipotent algebras ,Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Solvable algebras ,Mathematics - Rings and Algebras ,01 natural sciences ,Nilpotent ,Bracket (mathematics) ,Rings and Algebras (math.RA) ,Homogeneous ,Mathematics::Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Cartan matrix ,Kac-Moody algebras ,0101 mathematics ,Algebra over a field ,Element (category theory) ,Mathematics::Representation Theory ,17B67, 17B30 ,Mathematics - Abstract
Let $A$ be a symmetrisable generalised Cartan matrix, and let $\mathfrak g(A)$ be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak g(A)$: given two homogeneous elements $x,y \in \mathfrak g(A)$, when is their bracket $[x,y]$ a nonzero element? As an application of our results, we give a description of the solvable and nilpotent graded subalgebras of $\mathfrak g(A)$., 32 pages. Final version, to appear in Canadian Journal of Mathematics
- Published
- 2020
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