2011/10/31 by L Šnobl, Libor Snobl, Pavel Winternitz +1 · 4 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Affine Lie algebra #Algebraic structures and combinatorial models #Cartan subalgebra #Homotopy and Cohomology in Algebraic Topology #Indecomposable module #Killing form #Lie algebra #Lie conformal algebra #Simple Lie group #Subalgebra #math-ph #math.MP #msc:17B05 #msc:17B30 #msc:17B81
paper · pdf · doi:10.1088/1751-8113/45/9/095202
published in Journal of Physics A Mathematical and Theoretical 45(9), 095202 (Institute of Physics) · 22 pages; minor changes, mostly reformulations, typo corrections and added references
openalex publication_date 2012/02/20 · arxiv created 2012/03/13 · arxiv updated 2012/03/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras. Specifically in this paper, we consider a nilpotent Lie algebra that is isomorphic to the nilradical of the Borel subalgebra of a complex simple Lie algebra or of its split real form. We treat all the classical and exceptional simple Lie algebras in a uniform manner. We identify the nilpotent Lie algebra as the one that consists of all positive root spaces. We present general structural properties of all solvable extensions of . In particular, we study the extension by one non-nilpotent element and by the maximal number of such elements. We show that the extension of maximal dimension is always unique and isomorphic to the Borel subalgebra of the corresponding simple Lie algebra.