4 papers
Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals
Mikhail Borovoi, Willem A. de Graaf, Robert M. Guralnick
Following an idea of Demarche and using computer calculations of the authors and ideas of the LLM Claude Fable 5, we construct an explicit 10-dimensional complex two-step nilpotent…
Computing component groups of stabilizers of nilpotent orbit representatives
Emanuele Di Bella, Willem A. De Graaf
The theory of nilpotent orbits of simple Lie algebras has seen tremendous developments over the past decades. In this context an important role is played by the component group of…
Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8
Willem A. de Graaf, Alessio Marrani
We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefl…
2-generation of simple Lie algebras and free dense subgroups of algebraic groups
Alla S. Detinko, Willem A. de Graaf
We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are f…