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q-Deformation of the Krichever-Novikov Algebra
The recent focus on deformations of algebras called quantum algebras can be
attributed to the fact that they appear to be the basic algebraic structures
underlying an amazingly diverse set of physical situations. To date many
interesting features of these algebras have been found and they are now known
to belong to a class of algebras called Hopf algebras [1]. The remarkable
aspect of these structures is that they can be regarded as deformations of the
usual Lie algebras. Of late, there has been a considerable interest in the
deformation of the Virasoro algebra and the underlying Heisenberg algebra
[2-11]. In this letter we focus our attention on deforming generalizations of
these algebras, namely the Krichever-Novikov (KN) algebra and its associated
Heisenberg algebra.Comment: AmsTex. To appear in Letters in Mathematical Physic
Symmetric Multiplets in Quantum Algebras
We consider a modified version of the coproduct for \U(\su_q(2)) and show
that in the limit when , there exists an essentially
non-cocommutative coproduct. We study the implications of this
non-cocommutativity for a system of two spin- particles. Here it is shown
that, unlike the usual case, this non-trivial coproduct allows for symmetric
and anti-symmetric states to be present in the multiplet. We surmise that our
analysis could be related to the ferromagnetic and antiferromagnetic cases of
the Heisenberg magnets.Comment: Needs subeqnarray.sty. To be published in Mod Phys Lett.
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