Realisations of GLp,q(2)GL_{p,q}(2) quantum group and its coloured extension through a novel Hopf algebra with five generators

A novel Hopf algebra $( {\tilde G}_{r,s} )$, depending on two deformation parameters and five generators, has been constructed. This ${\tilde G}_{r,s}$ Hopf algebra might be considered as some quantisation of classical $GL(2) \otimes GL(1)$ group, which contains the standard $GL_q(2)$ quantum group (with $q=r^{-1}$) as a Hopf subalgebra. However, we interestingly observe that the two parameter deformed $GL_{p,q}(2)$ quantum group can also be realised through the generators of this ${\tilde G}_{r,s}$ algebra, provided the sets of deformation parameters $p,~q$ and $r,~s$ are related to each other in a particular fashion. Subsequently we construct the invariant noncommutative planes associated with ${\tilde G}_{r,s}$ algebra and show how the two well known Manin planes corresponding to $GL_{p,q}(2)$ quantum group can easily be reproduced through such construction. Finally we consider the `coloured' extension of $GL_{p,q}(2)$ quantum group as well as corresponding Manin planes and explore their intimate connection with the `coloured' extension of ${\tilde G}_{r,s}$ Hopf structure.Comment: 24 page

Effect of spin rotation coupling on spin transport

We have studied the spin rotation coupling(SRC) as an ingredient to explain different spin related issues. This special kind of coupling can play the role of a Dresselhaus like coupling in certain conditions. Consequently, one can control the spin splitting, induced by the Dresselhaus like term, which is unusual in semiconductor heterostucture. Within this framework, we also study the renormalization of the spin dependent electric field and spin current due to the $\vec{k} . \vec{p}$ perturbation, by taking into account the interband mixing in the rotating system. In this paper we predict the enhancement of the spin dependent electric field resulting from the renormalized spin rotation coupling. The renormalization factor of the spin electric field is different from that of the SRC or Zeeman coupling. The effect of renormalized SRC on spin current and Berry curvature is also studied. Interestingly, in presence of this SRC induced SOC it is possible to describe spin splitting as well as spin galvanic effect in semiconductors.Comment: 12 pages, no figures, Accepted for publication in Annals of Physic

GRB011211: An alternative interpretation of the optical and X-ray spectra in terms of blueshifts

The redshifts of the gamma ray burst (GRB) GRB 011211 has been determined as 2.14 from several absorption lines seen in the spectrum of its optical afterglow. The spectrum of its X-ray afterglow exhibited several emission lines,and their identification led to a mean redshift 1.862. A supernova model has been proposed based on the redshift of the GRB as 2.141. It is shown here that the redshift interpretation cannot explain the observed spectra, as some serious inconsistencies exist in the process of redshift determinations in spectra of both optical and X-ray afterglows. In view of that, an alternative interpretation of the spectra is presented in terms of blueshifts. Ejection mechanism is proposed as a possible scenario to explain the blueshifted spectrum.Comment: 26 pages, one table; in Canadian Journal of Physics, June 200