Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras ...

Central extensions of Lie algebras can be understood and classified by means of 2-cocycles. The Lie algebras we are interested in are "twisted forms" (defined by Galois descent) of algebras of the form g⊗ kR with g split ...

LetRn be the ring of Laurent polynomials in n variables over a field k of characteristic zero and letKn be its fraction field. Given a linear algebraic κ-groupG,we showthat aKn-torsor under G which is unramified with respect ...

We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction ...

We study étale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, ...

We develop a theory of relative Kähler differentials for Lie algebras. The main result is that the functor of relative differentials is representable, and that the universal object which represents it behaves properly with ...

The existence of nondegenerate invariant bilinear forms is one of the most important tools in the study of Kac-Moody Lie algebras and extended affine Lie algebras. In practice, these forms are created, or shown to exist, ...