Abelian ideals in a Borel subalgebra of a complex simple Lie algebra

By Ruedi Suter. 2002

64 citations recorded by the source corpus.

Let $\mathfrak{g}$ be a complex simple Lie algebra and $\mathfrak{b}$ a fixed Borel subalgebra of $\mathfrak{g}$. We describe the abelian ideals in $\mathfrak{b}$ in a uniform way, that is, independent of the classification of complex simple Lie algebras. As an application we derive a formula for the maximal dimension of a commutative Lie subalgebra of $\mathfrak{g}$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e36005831af617c1b97cc74fabcc67180094b477

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In Algebra and Number Theory

1. Manuel Ceballos
2. Dietrich Burde
3. Wolfgang Alexander Moens
4. Alice Fialowski

In Geometry and Topology

1. Manuel Ceballos
2. Dietrich Burde
3. Wolfgang Alexander Moens
4. Alice Fialowski

In Mathematical Physics

1. Manuel Ceballos
2. Dietrich Burde
3. Wolfgang Alexander Moens
4. Alice Fialowski

Citations in the corpus

• Abelian Ideals of Maximal Dimension for Solvable Lie Algebras (2009, background): “We have indeed α(s) = β(b), and this number can be computed purely in terms of certain root system invariants, see [20].”