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- Willem A. de Graaf
- ISSAC
- 1997

By Ado's theorem every nite dimensional Lie algebra over a eld of characteristic zero has a faithful nite dimensional representation. We consider the algorithmic problem of constructing such a representation for Lie algebras given by a multiplication table. An eeective version of Ado's theorem is proved.

- Willem A. de Graaf
- J. Symb. Comput.
- 2009

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 0, given its Lie algebra. Using this an algorithm is presented for finding a maximal reductive subgroup and the unipotent radical of an algebraic group.

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 decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We… (More)

- Willem A. de Graaf, Gábor Ivanyos, Lajos Rónyai
- Applicable Algebra in Engineering, Communication…
- 1996

We consider the algorithmic problem of computing Cartan subalgebras in Lie algebras over finite fields and algebraic number fields. We present a deterministic polynomial time algorithm for the case when the ground fieldk is sufficiently large. Our method is based on a solution of a linear algebra problem: the task of finding a locally regular element in a… (More)

- Willem A. de Graaf, Gábor Ivanyos, A. Küronya, Lajos Rónyai
- Applicable Algebra in Engineering, Communication…
- 1997

We consider the algorithmic problem of computing Levi decompositions in Lie algebras and Wedderburn–Malcev decompositions in associative algebras over the field of rational numbers. We propose deterministic polynomial time algorithms for both problems. The methods are based on the corresponding classical existence theorems. Computational experiences are… (More)

- Willem A. de Graaf
- Experimental Mathematics
- 2005

In this paper 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 dimensional solvable Lie algebras (over fields of any characteristic). Precise conditions for isomorphism are given. Solvable Lie algebras have been classified by G. M.… (More)

Let G be a unipotent algebraic subgroup of some GLm(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G ∩ GLm(Z). This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.

- Willem A. de Graaf, Jana Pílniková, Josef Schicho
- J. Symb. Comput.
- 2009

For a Del Pezzo surface of degree 8 given over the rationals we decide whether there is a rational parametrization of the surface and construct one in the affirmative case. We define and use the Lie algebra of the surface to reach the aim. The algorithm has been implemented in Magma.

- Karin Baur, Jan Draisma, Willem A. de Graaf
- Experimental Mathematics
- 2007

abstract We present an algorithm for computing the dimensions of higher secant varieties of minimal orbits. Experiments with this algorithm lead to many conjectures on secant dimensions, especially of Grassmannians and Segre products. For these two classes of minimal orbits, we also point out a relation between the existence of certain codes and… (More)

- Willem A. de Graaf, Werner Nickel
- J. Symb. Comput.
- 2002