Euklidischer Algorithmus und die Gruppe GL.
Every reasonably sized matrix group is a subgroup of S ∞
Every reasonably sized matrix group has an injective homomorphism into the group of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into .
Exact Borel subalgebras of quasi-heriditary algebras, I (with an appendix by Leonard Scott).
Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem
Research partially supported by INTAS grant 97-1644We consider the variety of (p + 1)-tuples of matrices Aj (resp. Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial centralizers of matrices...
Examples of tensor categories.
Excellent special orthogonal groups.
Exercises dyadiques.
Existence et équidistribution des matrices de dénominateur dans les groupes unitaires et orthogonaux
Soit un groupe défini sur les rationnels, simplement connexe, -quasisimple et compact sur . On étudie des suites de sous-ensembles des points rationnels de définis par des conditions sur leur projection dans le groupe des adèles finies de . Nous montrons dans ce cadre un résultat d’équirépartition vers la probabilité de Haar sur le groupe des points réels. On utilise pour cela des propriétés de mélange de l’action du groupe des points adéliques sur l’espace . Pour illustrer ce résultat,...
Expansion and random walks in : I
We prove that the Cayley graphs of are expanders with respect to the projection of any fixed elements in generating a Zariski dense subgroup.
Expansion and random walks in : II
Expansion in finite simple groups of Lie type
We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].
Expansion in , square-free
Let be a fixed symmetric finite subset of that generates a Zariski dense subgroup of when we consider it as an algebraic group over by restriction of scalars. We prove that the Cayley graphs of with respect to the projections of is an expander family if ranges over square-free ideals of if and is an arbitrary numberfield, or if and .
Explicit deformation of Galois representations.
Explizite Präsentation von Chevalleygruppen über Z.
Exploiting symmetry in electromagnetic imaging problems by using group representation theory.
Exponential sums for O¯(2n,q) and their applications
Exponentiations over the quantum algebra
We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra . We discuss two cases, according to whether the parameter is a root of unity. We show that the universal enveloping algebra of embeds in a non-principal ultraproduct of , where varies over the primitive roots of unity.
Exponents of almost simple groups and an application to the restricted Burnside problem.
Expression for a general element of an matrix.
Ext1 for Eyl modules of SL2 (K).