This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted ...

Given a finite-dimensional Lie algebra g, let Γo(g) be the set of irreducible g-modules with non-vanishing cohomology. We prove that a gmodule V belongs to Γo(g) only if V is contained in the exterior algebra of the solvable ...

The conjugacy of split Cartan subalgebras in the finite-dimensional simple case (Chevalley) and in the symmetrizable Kac–Moody case (Peterson–Kac) are fundamental results of the theory of Lie algebras. Among the Kac–Moody ...

We give some conditions under which no two non-conjugate projective representations, in an algebra, of a given group can become conjugate over a separable extension of the base field. In particular, we show this is always ...

We relate the Belavin–Drinfeld cohomologies (twisted and untwisted) that have been introduced in the literature to study certain families of quantum groups and Lie bialgebras over a non algebraically closed field K of ...

The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called Uq(sl(2)). Their example ...

That finite-dimensional simple Lie algebras over the complex numbers can be classified by means of purely combinatorial and geometric objects such as Coxeter-Dynkin diagrams and indecomposable irreducible root systems, is ...

In this article, we study the obstructions to the local-global principle for homogeneous spaces with connected or abelian stabilizers over finite extensions of the field C ((x; y)) of Laurent series in two variables over ...

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of ...

In this thesis we mainly prove two results in an algebro-geometric way: If one has a curve Γ of (honest) quadrisecant planes to the Kummer variety of an indecomposable principally abelian variety (X,Θ) then the curve Γ ...