After a brief review of some basic notions concerning 1–differentiable cohomology, named here d̃-cohomology, we introduce a Lichnerowicz d̃– cohomology in a classical way. Next, following the classical study of coeffective cohomology, a special attention is paid to the study of some problems concerning coeffective cohomology in the graded algebra of 1– differentiable forms. Also, the case of an a...

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics is determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and spanreachability in ter...

We introduce the concept of strongly r-matrix induced (SRMI) Poisson structure, report on the relation of this property with the stabilizer dimension of the considered quadratic Poisson tensor, and classify the Poisson structures of the Dufour-Haraki classification (DHC) according to their membership of the family of SRMI tensors. One of the main results of our work is a generic cohomological p...

The bilinear map whose domain and range are identical is called self-bilinear map. Once such kind of bilinear map exists, the multilinear map can be constructed easily by using self bilinear map as a component. Yamakawa et al. have introduced the first secure self-bilinear map with auxiliary information based on the integer factoring assumption in Crypto 2014. Inspired by their work, we find th...

Before we continue, we need to point out some properties of algebraic de Rham cohomology. In other words, we will first prove some of the axioms before introducing the trace map and cohomology classes. Note that the axioms of a Weil cohomology theory do not provide for the existence of cohomology groups defined for nonprojective varieties, but that we may use the fact that they are defined for ...

We construct a dGBV algebra from Dolbeault complex of any closed hyperkk ahler manifold. A Frobenius manifold structure on an neighborhood of the origin in Dolbeault cohomology then arises via Manin's generalization of Barannikov-Kontsevich's construction of formal Frobenius manifold structure on formal extended moduli space of a Calabi-Yau manifold. It is explained why these two kinds of forma...

HOMOTOPY THEORY AND GENERALIZED SHEAF COHOMOLOGY BY KENNETHS. BROWN0) ABSTRACT. Cohomology groups Ha(X, E) are defined, where X is a topological space and £ is a sheaf on X with values in Kan's category of spectra. These groups generalize the ordinary cohomology groups of X with coefficients in an abelian sheaf, as well as the generalized cohomology of X in the usual sense. The groups are defin...