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On the structure of Kac–Moody algebras
- Source :
- Canadian Journal of Mathematics, Vol. Volume 73, no. Issue 4, p. 1124-1152 (2021)
- Publication Year :
- 2020
- Publisher :
- Canadian Mathematical Society, 2020.
-
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 $\mathfrak g(A)$.<br />32 pages. Final version, to appear in Canadian Journal of Mathematics
- 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
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 73
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....1880bb3cca72b4e965a6c9c52e63f9b1