Related papers: From uncountable abelian groups to uncountable non…

We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…

An $S$-ring (Schur ring) is called central if it is contained in the center of the group ring. We introduce the notion of a generalized Schur group, i.e. such finite group that all central $S$-rings over this group are schurian. It…

This Bachelor's thesis studies Adelman's construction of the universal abelian category of an additive category. It furthermore extends the construction such that it also applies to transformations between additive functors.

Let $G$ be a nonabelian group. We say that $G$ has an abelian partition, if there exists a partition of $G$ into commuting subsets $A_1, A_2, \ldots, A_n$ of $G$, such that $|A_i|\geqslant 2$ for each $i=1, 2, \ldots, n$. This paper…

We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable…

We classify by numerical invariants the finite subgroups $H$ of a primary abelian group $G$ for which every homomorphism or monomorphism of $H$ into $G$, or every endomorphism of $H$, extends to an endomorphism of $G$. We apply these…

We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.

This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras…

In this short note we introduce the unconditional noncommutative motivic Galois groups and relate them with those of Andre-Kahn.

In this paper we study the existence of free non-abelian subgroups in non-central permutable subgroups of general skew linear groups and locally finite group algebras.

Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.

This paper introduces the concept of slender generalized groups, extending the classical notion of slender abelian groups to the setting of generalized groups (completely simple semigroups). We establish fundamental properties of slender…

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…

We generalize the theory of base norm spaces to the complex case, and further to the noncommutative setting relevant to `quantum convexity'. In particular, we establish the duality between complex Archimedean order unit spaces and complex…

This is a brief exposition of the mathematical themes that motivate the special programme at the Newton Institute in 2009. It is mostly intended for the general public having mathematical training up to the level of secondary school.

An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in…

This is the first draft of a set of lecture notes developed for one-half of a seminar on two approaches to the notion of "Abelian", namely those of universal algebra, and of category theory. The half pertaining to the universal-algebraic…

We introduce and study non-abelian cohomology sets of Hopf algebras with coefficients in Hopf comodule algebras. We prove that these sets generalize as well Serre's non-abelian group cohomology theory as the cohomological theory constructed…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

We obtain characterizations and structure results for homogeneous principal bundles over abelian varieties, that generalize work of Miyanishi and Mukai on homogeneous vector bundles. For this, we rely on notions and methods of algebraic…