We define the cohomological Burnside ring B(G,M) of a finite group G with coefficients in a ZG-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X(G,M). The cohomology groups H ∗ X(G,M) are defined in such a way that H∗ X(G, M) ∼= ⊕iH∗(Hi,M) when X is the disjoint union of transitive G-sets G/Hi. I...

We use group cohomology and the de Rham complex on simplicial manifolds to give explicit differential forms representing generators of the cohomology rings of moduli spaces of representations of fundamental groups of 2-manifolds. These generators are constructed using the de Rham representatives for the cohomology of classifying spaces BK where K is a compact Lie group; such representatives (un...

We follow the computations in [2], [5], and [8] to deduce the cohomology rings of various Lie groups (SU(n), U(n), Sp(n) with Z-coefficients and SO(n), Spin(n), G2, F4, E6, E7, E8 with field coefficients) using the Serre spectral sequence.

We give a refinement of Saito's arithmetic duality for two-dimensional local rings by giving algebraic group structures cohomology groups.

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...