To a compact Lie group $G$ one can associate space $E(2,G)$ akin to the poset of cosets abelian subgroups discrete group. The was introduced by Adem, F. Cohen and Torres-Giese, subsequently studied Adem G\'omez, other authors. In this short note, we prove that is if only $\pi_i(E(2,G))=0$ for $i=1,2,4$. This analogue fact simply--connected abelian.

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

The group properties of the shallow-water equations with complete Coriolis force is subject this study. In particular we apply Lie theory to classify system three nonlinear partial differential according admitted point symmetries. For each case classification problem one-dimensional optimal determined. results are applied for derivation new similarity solutions.

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

Cyclotron resonant wave-particle interactions are studied in the context of Hamiltonian theory with utilization of Lie transform techniques. The canonical perturbation method for single particle motion is used for providing results for the collective particle behavior under interaction with wave fields of either localized or periodic profiles. Analytical expressions for the calculation of phase...

Abstract Stratified groups are those simply connected Lie whose algebras admit a derivation for which the eigenspace with eigenvalue 1 is generating. When stratified group equipped left-invariant path distance that homogeneous respect to automorphisms induced by derivation, this metric space known as Carnot group. appear in several mathematical contexts. To understand their algebraic structure,...