Unitary representations of the fundamental group of a Kähl-er manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to poly-stable Higgs bundles. In this paper we find the objects corresponding to affine representations: the linear part gives a Higgs bundle and the translation part corresponds to an element of a generalized...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

in this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎after we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎we also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎as the second part of the work‎, ‎we define the notion...

This thesis contains various results on unitary 2-representations of nite groups and their 2-characters, as well as on pivotal structures for fusion categories. The motivation is extended topological quantum eld theory (TQFT), where the 2-category of unitary 2-representations of a nite group is thought of as the `2-category assigned to the point' in the untwisted nite group model. The rst resul...

My main project to date ([3]) is concerned with certain moduli spaces of Higgs bundles and isomorphisms between them, which arise from natural operations on the bundles. Conventionally1, a Higgs bundle is a pair (V, φ) on a Riemann surface X. Here V is a vector bundle (algebraic) and φ is a linear map V → ΩX⊗V called the Higgs field. Why consider such pairs? If nothing else, maybe a Higgs bundl...

Let E 1, . . . , Ek and E be natural vector bundles defined over the category Mf m of smooth oriented m–dimensional manifolds and orientation preserving local diffeomorphisms, with m ≥ 2. Let M be an object of Mf m which is connected. We give a complete classification of all separately continuous k–linear operators D : Γc(E1M) × . . . × Γc(EkM) → Γ(EM) defined on sections with compact supports,...

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a perfect complex on a ringed space. Subject classification: 16E40 (Primary), 18E30, 14F05 (Secondary).