2022/01/21 by Dietrich Burde, Burde, Dietrich, Wolfgang Alexander Moens +1
Mathematics · Chemistry · #Advanced Topics in Algebra #Chemical Synthesis and Reactions #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2201.08758
We study \em disemisimple Lie algebras, i.e., Lie algebras which can be written as a vector space sum of two semisimple subalgebras. We show that a Lie algebra \mathfrakg is disemisimple if and only if its solvable radical coincides with its nilradical and is a prehomogeneous \mathfraks-module for a Levi subalgebra \mathfraks of \mathfrakg. We use the classification of prehomogeneous \mathfraks-modules for simple Lie algebras \mathfraks given by Vinberg to show that the solvable radical of a disemisimple Lie algebra with simple Levi subalgebra is abelian. We extend this result to disemisimple Lie algebras having no simple quotients of type A.