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Abstract

Chains of extended twists are composed of factors Fk=FekFJk\mathcal{F}_k=\Phi_{\varepsilon _k}\Phi_{\mathcal{J}_k} . The set of Jordanian twists { FJk \Phi _{\mathcal{J}_k } } can be applied to the initial Hopf algebra FJk ¼FJ1 FJ0 :A ® AJk ¼J0 \Phi _{\mathcal{J}_k } \cdots \Phi _{\mathcal{J}_1 } \Phi _{\mathcal{J}_0 } :\mathcal{A} \to \mathcal{A}_{\mathcal{J}_k \cdots \mathcal{J}_0 } . In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when A = U(sl(N))\mathcal{A} = U(sl(N)) .

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