Schur's theorem and its generalisation, Baer's theorem, are distinguished results in group theory, connecting the upper central quotients with lower series. The aim of this paper is to generalise these two different directions, using novel methods related non-abelian tensor product. In particular, we prove a version Schur–Baer for finitely generated groups. Then, apply newly obtained describe k...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

let g be a simple connected graph. the generalized polarity wiener index ofg is defined as the number of unordered pairs of vertices of g whosedistance is k. some formulas are obtained for computing the generalizedpolarity wiener index of the cartesian product and the tensor product ofgraphs in this article.

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

We consider a Yang–Mills theory in loop space with an affine Lie gauge group. The Chapline–Manton coupling, the coupling between Yang–Mills fields and an abelian antisymmetric tensor field of the second rank via the Chern– Simons term, is systematically derived within the framework of the Yang–Mills theory. The generalized Chapline–Manton couplings, the couplings among nonabelian tensor fields ...

We compute the multiplicity of irreducible representations in decomposition tensor product an arbitrary number n fundamental SU(N), and we identify a duality representation content this decomposition. Our method utilizes mapping SU(N) to states free fermions on circle, can be viewed as random walk multidimensional lattice. also derive large-n limit response system external non-abelian magnetic ...

We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including transition non-Abelian chiral spin liquid. Using loop gas and string states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on star lattice Kitaev model as an example, we compute overlap minimally entangled through transfer matrices. demons...

We extend the definition, from the class of abelian groups to a general locally compact group G, of Feichtinger’s remarkable Segal algebra S0(G). In order to obtain functorial properties for non-abelian groups, in particular a tensor product formula, we endow S0(G) with an operator space structure. With this structure S0(G) is simultaneously an operator Segal algebra of the Fourier algebra A(G)...