With the classical assumptions on f , a convergence criterion of Newton’s method (independent of affine connections) to find zeros of a mapping f from a Lie group to its Lie algebra is established, and estimates of the convergence domains of Newton’s method are obtained, which improve the corresponding results in (Owren and Welfert, The Newton iteration on Lie groups, BIT, Numer., 2000, 40(2), ...

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the involved Lie group by a central extension of it. The geometric techniques devel...

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

Algebraic groups are analogues of the classical Lie groups, such as the linear, orthogonal or symplectic groups, over arbitrary algebraically closed fields. Hence they are no longer classical manifolds, but varieties in the sense of algebraic geometry. In particular, they are used in the uniform description of the finite groups of Lie type, which encompass a substantial part of all finite simpl...

Superimposed D–branes have matrix–valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativi...

The Berezin quantization on a simply connected homogeneous Kähler manifold, which is considered as a phase space for a dynam-ical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic functions corresponding to generalized coherent states. The Lie algebra associated with the manifold symmetry group is given in terms of first-order differentia...

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classical Routh reduction, which we show is naturally posed in this fibered setting. ...

This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.

We compute the $O(1/N^3)$ correction to critical exponent $\eta$ in chiral XY or Gross-Neveu model $d$-dimensions. As leading order vertex anomalous dimension vanishes, direct application of large $N$ conformal bootstrap formalism is not immediately possible. To circumvent this we consider more general Nambu-Jona-Lasinio for a non-abelian Lie group. Taking abelian limit exponents produces those...

A symplectic Lie group is a with left-invariant form. Its algebra structure that of quasi-Frobenius algebra. In this note, we identify the groupoid analogue group. We call aforementioned \textit{$t$-symplectic groupoid}; $t$ motivated by fact each target fiber $t$-symplectic manifold. For $\mathcal{G}\rightrightarrows M$, show there one-to-one correspondence between algebroid structures on $A\m...