Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume is an attempt to provide an overview of some of the recent advances in representation theory from a geometric standpoint. A geometrically-oriented treatment is very timely and has long been desired, especially since the discovery of D-modules in the early '80s and the quiver approach to quantum groups in the early '90s.

Group theory --- Algebraic geometry --- Differential geometry. Global analysis --- Ordered algebraic structures --- Géométrie différentielle --- Géométrie algébrique --- Représentations de groupes --- Variétés symplectiques --- Geometry, Differential --- Symplectic manifolds --- Representations of groups --- Geometry, Algebraic --- 514.1 --- 514.1 General geometry --- General geometry --- Manifolds, Symplectic --- Manifolds (Mathematics) --- Group representation (Mathematics) --- Groups, Representation theory of --- Differential geometry --- Geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use of Laurent's interpolation determinants. The most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups

Approximatie [Diophantische ] --- Approximation [Diophantienne ] --- Approximation [Diophantine ] --- Diophantine approximation --- Groupes algébraïques linéaires --- Lineaire algebraïsche groepen --- Linear algebraic groups --- Diophantine approximation. --- Linear algebraic groups. --- 512.74 --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Approximation, Diophantine --- Approximation theory --- Diophantine analysis --- Algebraic groups. Abelian varieties --- 512.74 Algebraic groups. Abelian varieties --- Mathematics --- Number theory --- Mathématiques --- Géométrie algébrique --- Théorie des groupes --- Théorie des nombres --- Algebra. --- Number theory. --- Algebraic geometry. --- Group theory. --- Number Theory. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Mathematical analysis