Let G be a finite group, F an algebraically closed field of finite characteristic p, and let B be a block of FG. We show that the Hochschild and Linckelmann cohomology rings of B are isomorphic, modulo their radicals, in the cases where (1) B is cyclic and (2) B is arbitrary and G either a nilpotent group or a Frobenius group (p odd). (The second case is a consequence of a more general result)....

The purpose of this paper is to introduce a cohomology theory for abelian matched pairs of Hopf algebras and to explore its relationship to Sweedler cohomology, to Singer cohomology and to extension theory. An exact sequence connecting these cohomology theories is obtained for a general abelian matched pair of Hopf algebras, generalizing those of Kac and Masuoka for matched pairs of finite grou...

The cohomology of arithmetic groups is made up of two pieces, the cuspidal and noncuspidal parts. Within the cuspidal cohomology is a subspace— the /-cuspidal cohomology—spanned by the classes that generate representations of the associated finite Lie group which are cuspidal in the sense of finite Lie group theory. Few concrete examples of /-cuspidal cohomology have been computed geometrically...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

Let G be an exceptional Lie group with T ⊂ G a maximal torus. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...