Peripheric Extended Twists

Abstract

The properties of the set L of extended jordanian twists are studied. It is shown that the boundaries of L contain twists whose characteristics differ considerably from those of internal points. The extension multipliers of these "peripheric" twists are factorizable. This leads to simplifications in the twisted algebra relations and helps to find the explicit form for coproducts. The peripheric twisted algebra U(sl(4)) is obtained to illustrate the construction. It is shown that the corresponding deformation U_{P}(sl(4)) cannot be connected with the Drinfeld--Jimbo one by a smooth limit procedure. All the carrier algebras for the extended and the peripheric extended twists are proved to be Frobenius.

16 pages, LaTeX 209. Some misprints have been corrected and new Comments added

References in corpus (4)

• Deformed Yangians and Integrable Models
• Classical and quantum duality in jordanian quantizations
• BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle
• Twisted h-spacetimes and invariant equations

Cited by in corpus (13)

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• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• Extended and Reshetikhin Twists for sl(3)
• Twisted Conformal Algebra so(4,2)
• Quantization of Lie-Poisson structures by peripheric chains
• Basic Twist Quantization of the Exceptional Lie Algebra G_2
• Twist of Lie algebras by 6 dimensional subalgebra
• Extensions of Peripheric Extended Twists and Inhomogeneous Lie Algebras
• Twists in U(sl(3)) and their quantizations
• On super-Jordanian ${\mathcal{U}}_{\mathsf{h}}(sl(N|1))$ algebra