Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras

Links, Jon; Gould, M. D.; Zhang, Yao-Zhong

doi:10.1063/1.533390

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2005

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Cited by 19 publications

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“…QHA are the underlying algebraic structures of elliptic quantum groups [8,9,10,11,14,20] and hence have an important role in obtaining solutions to the dynamical Yang-Baxter equation. They arise in conformal field theory [3,4], algebraic number theory [7] and in the theory of knots [1,15,16].…”

Section: Introductionmentioning

confidence: 99%

Some twisted results

Gould¹,

Lekatsas²

2005

J. Phys. A: Math. Gen.

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The Drinfeld twist for the opposite quasi-Hopf algebra, H cop is determined and is shown to be related to the (second) Drinfeld twist on a quasi-Hopf algebra. The twisted form of the Drinfeld twist is investigated. In the quasi-triangular case it is shown that the Drinfeld u operator arises from the equivalence of H cop to the quasi-Hopf algebra induced by twisting H with the R-matrix. The Altschuler-Coste u operator arises in a similar way and is shown to be closely related to the Drinfeld u operator. The quasi-cocycle condition is introduced, and is shown to play a central role in the uniqueness of twisted structures on quasi-Hopf algebras. A generalisation of the dynamical quantum Yang-Baxter equation, called the quasi-dynamical quantum Yang-Baxter equation is introduced.

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