My question is about Kac-Moody (KM) algebras of finite rank with symmetrized Cartan matrices $B = C A$ ($A$ is Cartan matrix) of signatures $(-,-,+,...,+)$, $(-,-,-,+,...,+)$, etc. i.e. with $2$, $3$ and so on time-like directions. It will be of interest to find in literature the study of such algebras, or, at least, examples of Cartan matrices $A$, especially of rank $3$ and signature $(-,-,+)$ and of rank $4$ and signature $(-,-,+,+)$. What is known about classification of such ``extra-Lorentzian'' KM algebras?
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