let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

In the paper about the cryptosystem MST3, Svaba and Trung proposed a way to build a cryptosystem based on the concept of logarithmic signatures, and they choose Suzuki’s group, which is not abelian for implementing. Recently, to reason why these methods cannot be applied to abelian groups; Svaba, Trung and Wolf developed some algorithms to factorize the fused transversal logarithmic signatures ...

We construct a (0, 2), D = 2 gauged linear sigma model on a supermanifold in both the Abelian gauge group and the non-Abelian gauge group. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operatorˆU for the Abelian gauge group. Thê U operator provides consistency conditions for satisfying the SUSY invariance. C...

Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF) as zero-energy quasi-particle at the cores. However, in experiments it is difficult to manipulate vortices. In the present work, we propose a way to braid MFs without moving vortices. The only operation required in the present scheme is to turn on and off l...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quas...

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

We study analogues of the radial subalgebras in free group factors (called algebras class functions) setting compact quantum groups. For orthogonal groups we show that they are not MASAs, as soon a non-Kac situation. The most important notion to our present work is (quasi-)split inclusion. prove inclusion algebra functions quasi-split for some unitary – this case subalgebra non-abelian and also...

We initiate the large scale geometric study of Banach-Lie groups, especially linear groups. show that exponential length, originally introduced by Ringrose for unitary groups $C^*$-algebras, defines quasi-isometry type any connected group. As an illustrative example, we consider separable abelian unital $C^*$-algebras with spectrum having finitely many components, which classify up to topologic...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Abstract We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly expansions the second kind densely linearly ordered abelian groups. derive basic dimension a set definable in including addition property, which is equality for maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds also demonst...