Related papers: Real structures on primary Hopf surfaces

We start to study the problem of classifying smooth proper varieties over a field k from the standpoint of A^1-homotopy theory. Motivated by the topological theory of surgery, we discuss the problem of classifying up to isomorphism all…

Hopf algebroids are generalization of Hopf algebras over non-commutative base rings. It consists of a left- and a right-bialgebroid structure related by a map called the antipode. However, if the base ring of a Hopf algebroid is commutative…

In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph…

We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic group up to add extra formal diffeomorphisms. We show that this is the case for…

Let $H_{g}$ be a 3-dimensional handlebody of genus $g$. We determine the twisted first homology group of the mapping class group of $H_{g}$ with coefficients in the first integral homology group of the boundary surface $\partial H_{g}$ for…

We develop in this paper the theory of covers for Hausdorff properly $\bigvee $-definable manifolds with definable choice in an o-minimal structure $\N$. In particular, we show that given an $\N$-definably connected $\N$-definable group $G$…

We study three dimensional real hypersurfaces in CP^2 and CH^2 equipped with $xi$-parallel structure Jacobi operator. We prove that they are Hopf hypersurfaces and if additional $\alpha\neq0$, we classify them.

We characterize Hopf spaces with finitely generated cohomology as an algebra over the Steenrod algebra. We "deconstruct" the original space into an H-space Y with finite mod p cohomology and a finite number of p-torsion Eilenberg-Mac Lane…

In this article, we prove that any complex smooth rational surface $X$ which has no automorphism of positive entropy has a finite number of real forms (this is especially the case if $X$ cannot be obtained by blowing up $\mathbb…

Real forms of a complex reductive group are classified in terms of Galois cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group. Alternatively, the theory of the Cartan involution gives a description in terms of cohomology…

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…

English abstract: This work contains of five chapters: The first one deals with Morita equivalence of star algebras. In particular star algebras which are equipped with a symmetry given by a Hopf (star-) algebra. In the second chapter we…

Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…

We address a conjecture that $\pi_1$-surjective maps between closed aspherical 3-manifolds having the same rank on $\pi_1$ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first…

Let $G$ be a compact connected Lie group with $\pi_1(G)\cong\mathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of…

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…

Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable extension of local fields, $\left[ L:K\right] =p^{n},\;n\geq2.$ It is known that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act on the…

In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which…

Let $p$ be a strong type of an algebraically closed tuple over $B=\acl^{\eq}(B)$ in any theory $T$. Depending on a ternary relation $\indo^*$ satisfying some basic axioms (there is at least one such, namely the trivial independence in $T$),…