We develop a theory of ‘non-abelian higher special elements’ in the non-commutative exterior powers Galois cohomology p-adic representations. explore their relation to organising matrices and thus module structure Selmer modules. In concrete applications, we relate our general formulation refined conjectures Birch Swinnerton-Dyer type Tate–Shafarevich groups abelian varieties.

If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by EX . In the present work we establish a topological classification of such bundles in terms of the first cohomology group of X with coefficients in the ring Z2.

A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal 2-algebras and crossed modules 3-Lie are interpreted by using lower degree groups.

By work of Farinati, Solberg, and Taillefer, it is known that the Hopf algebra cohomology a quasi-triangular algebra, as graded Lie under Gerstenhaber bracket, abelian. Motivated by question whether this holds for nonquasi-triangular algebras, we show brackets on can be expressed via an arbitrary projective resolution using Volkov's homotopy liftings generalized to some exact monoidal categorie...

We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes’ cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Künneth and Mayer–Vietoris sequences. The second way involves a chain complex of ordered ...

Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π1 which are in some sense obtained by extensions—nonabelian Hodge theory concerns the cohomology of a variety with nonabelian coefficients. Because of the basic fact that homotopy groups in higher dimensions are abelian, and si...

A coring approach to non-Abelian descent cohomology of [P. Nuss & M. Wambst, Non-Abelian Hopf cohomology, Preprint arXiv:math.KT/0511712, (2005)] is described and a definition of a Galois cohomology for partial group actions is proposed.

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach–Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.