The Lagrange-d’Alembert equations of a non-holonomic system with symmetry can be reduced to the Lagrange-d’Alembert-Poincaré equations. In a previous contribution we have shown that both sets of equations fall in the category of so-called ‘Lagrangian systems on a subbundle of a Lie algebroid’. In this paper, we investigate the special case when the reduced system is again invariant under a new ...

The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this c-duality are identified and they are placed in the context of Harish-Chandra’s legacy for the unitary representations program. Our paper begins with a discussion of path spac...

We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. present explicit examples of infinite dimensional braided Lie and algebras infinitesimal gauge transformations on spheres. The braiding these is implemented by the structure symmetry systematic analysis compatible $*$-structures, encompassing quasitriangular case.

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group G. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundl...

Lie transformation groups containing a one-dimensional subgroup acting cyclically on a manifold are considered. The structure of the group is found to be considerably restricted by the existence of a one-dimensional subgroup whose orbits are circles. The results proved do not depend on the dimension of the manifold nor on the existence of a metric, but merely on the fact that the Lie group acts...

We obtain solutions of the time-dependent Einstein Field Equations which satisfy Karmarkar condition via method Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal flatness, Weyl-free collapse and shear-free collapse. In particular, a solution was found satisfies heat-flux boundary Santos, radiating stellar model then obtained investiga...