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On the structure of Kac–Moody algebras
Published online by Cambridge University Press: 20 May 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
$\mathfrak {g}(A)$
.
MSC classification
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- Copyright
- © Canadian Mathematical Society 2020
Footnotes
F.R.S.-FNRS post-doctoral researcher.
References
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