609 research outputs found
Realisations of quantum group and its coloured extension through a novel Hopf algebra with five generators
A novel Hopf algebra , depending on two deformation
parameters and five generators, has been constructed. This
Hopf algebra might be considered as some quantisation of classical group, which contains the standard quantum group
(with ) as a Hopf subalgebra. However, we interestingly observe
that the two parameter deformed quantum group can also be
realised through the generators of this algebra, provided
the sets of deformation parameters and are related to each other
in a particular fashion. Subsequently we construct the invariant noncommutative
planes associated with algebra and show how the two well
known Manin planes corresponding to quantum group can easily be
reproduced through such construction. Finally we consider the `coloured'
extension of quantum group as well as corresponding Manin planes
and explore their intimate connection with the `coloured' extension of Hopf structure.Comment: 24 page
Algebraic aspect and construction of Lax operators in quantum integrable systems
An algebraic construction more general and intimately connected with that of
Faddeev, along with its application for generating different classes of
quantum integrable models are summarised to complement the recent results of
ref. 1 ( L.D. Faddeev, {\it Int. J. Mod. Phys. } {\bf A10}, 1845 (1995) ).Comment: 8 pages, plain TEX, no figure
Construction of some special subsequences within a Farey sequence
Recently it has been found that some special subsequences within a Farey
sequence play a crucial role in determining the ranges of coupling constant for
which quantum soliton states can exist for an integrable derivative nonlinear
Schrodinger model. In this article, we find a novel mapping which connects two
such subsequences belonging to Farey sequences of different orders. By using
this mapping, we construct an algorithm to generate all of these special
subsequences within a Farey sequence. We also derive the continued fraction
expansions for all the elements belonging to a subsequence and observe a close
connection amongst the corresponding expansion coefficients.Comment: latex, 8 page
Multiparametric and coloured extensions of the quantum group and the Yangian algebra through a symmetry transformation of the Yang-Baxter equation
Inspired by Reshetikhin's twisting procedure to obtain multiparametric
extensions of a Hopf algebra, a general `symmetry transformation' of the
`particle conserving' -matrix is found such that the resulting
multiparametric -matrix, with a spectral parameter as well as a colour
parameter, is also a solution of the Yang-Baxter equation (YBE). The
corresponding transformation of the quantum YBE reveals a new relation between
the associated quantized algebra and its multiparametric deformation. As
applications of this general relation to some particular cases, multiparametric
and coloured extensions of the quantum group and the Yangian algebra
are investigated and their explicit realizations are also discussed.
Possible interesting physical applications of such extended Yangian algebras
are indicated.Comment: 21 pages, LaTeX (twice). Interesting physical applications of the
work are indicated. To appear in Int. J. Mod. Phys.
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