Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking th...

3D electroweak sphaleron configurations are studied by Abelian projection from the Maximal Abelian gauge. They all contain a symmetric array of Abelian monopoles and anti-monopoles connected by Abelian vortex strings. Gauge–invariant lattice definitions of the Nambu monopole and the Z–vortex string on the lattice are formulated. Looking for these new types of lattice topological defects, we dem...

We do not have much intuition in nonabelian theories, whereas our understanding of the Maxwell equations and abelian theories is far better. For this reason people are trying to explain the confinement phenomenon in terms of the abelian projection of nonabelian theory [1]. Different abelian projections lead to different abelian theories, and now it is clear that there exist at least one abelian...

In this paper we introduce non-abelian zeta functions and more generally non-abelian L-functions for number fields, based on geo-arithmetical cohomology, geo-arithmetical truncation and Langlands’ theory of Eisenstein series. More precisely, in Chapter I, we start with a new yet natural geo-arithmetical cohomology and a geo-arithmetical stability in order to define genuine non-abelian zeta func...

let $g$ be a non-abelian group. the non-commuting graph $gamma_g$ of $g$ is defined as the graph whose vertex set is the non-central elements of $g$ and two vertices are joined if and only if they do not commute.in this paper we study some properties of $gamma_g$ and introduce $n$-regular $ac$-groups. also we then obtain a formula for szeged index of $gamma_g$ in terms of $n$, $|z(g)|$ and $|g|...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain at most Θ(n) distinct factors, and there exist words of length n containing Θ(n) distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length n grow...

We give a gauge-independent definition of Abelian dominance in the Wilson loop operator and a constructive proof of the Abelian dominance through a non-Abelian Stokes theorem via lattice regularization. We obtain a necessary and sufficient condition for the Abelian dominance in the Wilson loop operator in the fundamental representation. In the continuum limit, the gauge field is decomposed such...