Solvable Lie algebras with Borel nilradicals

Details Solvable Lie algebras with Borel nilradicals Solvable Lie algebras with Borel nilradicals

2011-10-25

arxiv.org/abs/1110.5492v2

J. Phys. A: Math. Theor. 45 (2012) 095202

Physics

Mathematical Physics

22 pages; minor changes, mostly reformulations, typo corrections and added references

Scientific paper

10.1088/1751-8113/45/9/095202

The present article 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 article we consider a nilpotent Lie algebra n 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 classical and exceptional simple Lie algebras in a uniform manner. We identify the nilpotent Lie algebra n as the one consisting of all positive root spaces. We present general structural properties of all solvable extensions of n. In particular, we study the extension by one nonnilpotent 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.

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