Quantum tori and the structure of elliptic quasi-simple Lie algebras
\textit{R. Høegh-Krohn} and \textit{B. Torresani} [J. Funct. Anal. 89, 106-136 (1990; Zbl 0792.17019)] gave a complete classification of the root systems of the irreducible quasi-simple Lie algebras of elliptic type. Now let \(L\) be such an algebra which is also simply laced. The authors introduce the property of tameness and show examples of both tame and wild algebras. The core \(C\) of \(L\) is defined to be the subalgebra of \(L\) generated by the non-isotropic root spaces. \(C\) is an ideal and the natural representation of \(L\) on \(C\) is investigated and coordinates identified when rank \(L\geq 3\). The universal central extensions and derivation algebra of the core are studied and it is found that \(L\) is roughly the semi-direct product of \(C\) with an algebra of skew-symmetric outer derivations. Thus the authors give a classification of the tame irreducible elliptic quasi-simple Lie algebras which are simply laced and rank greater than or equal to 3.
tame irreducible elliptic quasi-simple Lie algebras
scientific article; zbMATH DE number 847484