Peripheric Extended Twists

Details Peripheric Extended Twists Peripheric Extended Twists

1998-11-25

arxiv.org/abs/math/9811153v2

Mathematics

Quantum Algebra

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

Scientific paper

10.1088/0305-4470/32/24/316

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.

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