112 citations · 144 across the 22 of their papers we have counts for
23 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…
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 non-degenerate two-step nilpotent Lie algebras of dimension eight
Mikhail Borovoi, Bogdan Adrian Dina, Willem A. de Graaf
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure…
Computing Galois cohomology of a real linear algebraic group
Mikhail Borovoi, Willem A. de Graaf
Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois…
Exploring Lie theory with GAP
Willem A. de Graaf
We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained usi…
Semisimple elements and the little Weyl group of real semisimple -graded Lie algebras
Willem de Graaf, Hông Vân Lê
We consider the semisimple orbits of a Vinberg -representation. First we take the complex numbers as base field. By a case by case analysis we show a technical result stating th…
Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces
Maciej Bochenski, Willem A. de Graaf, Piotr Jastrzebski +1
We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new ex…
Classification of four qubit states and their stabilisers under SLOCC operations
Heiko Dietrich, Willem A. de Graaf, Alessio Marrani +1
We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group on the Hilbert space $\mathcal{H}_4 = (\ma…
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…
Nilpotent orbits in real symmetric pairs and stationary black holes
Heiko Dietrich, Willem A. de Graaf, Daniele Ruggeri +1
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In t…
Regular subalgebras and nilpotent orbits of real graded Lie algebras
H. Dietrich, Paolo Faccin, Willem A. de Graaf
For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphis…
irrep decompositions of interest for physical models
Lorenzo Fortunato, Willem A. de Graaf
In this note we show how to obtain the projection matrix for the chain and we tabulate some decompositions of the symplectic algebra representations i…
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…
An effective method to compute closure ordering for nilpotent orbits of -representations
W. A. de Graaf, E. B. Vinberg, O. S. Yakimova
We develop an algorithm for computing the closure of a given nilpotent -orbit in $\g_1$, where $\g_1$ and are coming from a or a -grading $\g= \bigoplus \g_…
Angular momentum non conserving symmetries in bosonic models
L. Fortunato, W. A. de Graaf
The Levi-Malcev decomposition is applied to bosonic models of quantum mechanics based on unitary Lie algebras u(2), u(2)+u(2), u(3) and u(4) to clearly disentangle semisimple subal…
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…
Good index behaviour of -representations, I
Willem A. de Graaf, Oksana S. Yakimova
Let be an algebraic group with $q=\Lie Q$ and a -module. The index of is the minimal codimension of the -orbits in the dual space . There is a general inequa…
Computing with nilpotent orbits in simple Lie algebras of exceptional type
Willem de Graaf
Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classifi…