112 citations · 144 across the 22 of their papers we have counts for
9 papers · 1 filter
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…
A computational approach to almost-inner derivations
Heiko Dietrich, Willem A. de Graaf
We present a computational approach to determine the space of almost-inner derivations of a finite dimensional Lie algebra given by a structure constant table. We also present an e…
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…
Constructing semisimple subalgebras of real semisimple Lie algebras
Paolo Faccin, Willem A. de Graaf
We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our method…
Six-dimensional nilpotent Lie algebras
Serena Cicalo, Willem A de Graaf, Csaba Schneider
We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To…
Classification of nilpotent associative algebras of small dimension
Willem A. de Graaf
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras o…
Computations with reachable elements in simple Lie algebras
Willem de Graaf
We report on some computations with reachable elements in simple Lie algebras of exceptional type within the SLA package of GAP4. These computations confirm the classification of s…
Constructing semisimple subalgebras of semisimple Lie algebras
Willem A. de Graaf
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have be…