Absence of functional FMRP causes Fragile X syndrome. Abnormalities in synaptic processes in the cerebral cortex and hippocampus contribute to cognitive deficits in Fragile X patients. So far, the potential roles of cerebellar deficits have not been investigated. Here, we demonstrate that both global and Purkinje cell-specific knockouts of Fmr1 show… (More)
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.
First we describe the Skjelbred-Sund method for classifying nilpotent Lie algebras. Then we use it to classify 6-dimensional nilpotent Lie algebras over any field of characteristic not 2. The proof of this classification is essentially constructive: for a given 6-dimensional nilpotent Lie algebra L, following the steps of the proof, it is possible to find a… (More)
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)
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 classified. We describe a simple algorithm for finding a representative of a nilpotent orbit. We use this to compute lists of representatives of these orbits for the Lie algebras of… (More)
We consider the algorithmic problem of computing Levi decomposi-tions 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)
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)