In a three-volume work, Strade classifies the simple Lie algebras over an

algebraically closed field of characteristic p equal to or larger than 3, in the sense that he presents a list of simple Lie algebras and a proof that this list is complete.

Throughout H is a d-dimensional semisimple Hopf algebra over an

algebraically closed field k of characteristic 0 and H* is its dual which is a semisimple Hopf algebra as well.

Let K be an

algebraically closed field with a complete and non-Archimedean norm [absolute value of (*)].

Throughout this paper, k is an

algebraically closed field, A is a finite dimensional k-algebra.

Now let K denote an

algebraically closed field of characteristic 0 with K[x] the corresponding polynomial ring and

Let n be a positive integer, and let V be a 2n-dimensional vector space over an

algebraically closed field K of characteristic 0.

Throughout this paper K is an

algebraically closed field of characteristic 0.

When X is a non-singular projective variety defined over an

algebraically closed field k of characteristic 0 and G is a connected reductive algebraic group over k, moduli spaces of (semi)stable principal G-bundles over X are known to exist and to be quasi-projective schemes (usually singular).

Let F be a fixed

algebraically closed field of characteristic 0.

In this section we explain how the trace map on the second cohomology of a curve over an

algebraically closed field k can be obtained as a special case of the construction in section 1.

We work over an

algebraically closed field k of characteristic p [not equal to] 2.

Let k be an

algebraically closed field of characteristic 0, let A be a reduced Noetherian k-algebra, and let (M, [nabla]) be a finitely generated torsion free A-module of rank one with a (not necessarily integrable) connection.