4 citations · 6 across the 6 of their papers we have counts for
6 papers
Computing faithful representations for nilpotent Lie algebras
Dietrich Burde, Bettina Eick, Willem de Graaf
We describe three methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods in…
Constructing arithmetic subgroups of unipotent groups
Willem de Graaf, Andrea Pavan
Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This…
Constructing algebraic groups from their Lie algebras
Willem de Graaf
A connected algebraic group in characteristic 0 is uniquely determined by its Lie algebra. In this paper an algorithm is given for constructing an algebraic group in characteristic…
A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces
Willem A. de Graaf, Michael Harrison, Jana Pilnikova +1
It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to d…
Classification of solvable Lie algebras
W. A. de Graaf
We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimen…
Constructing homomorphisms between Verma modules
W. A. de Graaf
A practical method for constructing a nontrivial homomorphsim between Verma modules is described.