On Quasi-Hopf superalgebras

dc.creatorGould, Mark D.
dc.creatorZhang, Yao-Zhong
dc.creatorIsaac, Phillip S.
dc.date1998-11-10
dc.date1998-11-19
dc.date.accessioned2026-07-07T05:26:48Z
dc.date.available2026-07-07T05:26:48Z
dc.descriptionIn this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot theory and integrable systems. In particular we introduce the opposite structure and prove in detail (for the graded case) Drinfeld's result that the coproduct $Δ' \equiv (S\otimes S)\cdot T\cdot Δ\cdot S^{-1}$ induced on a QHSA is obtained from the coproduct $Δ$ by twisting. The corresponding ``Drinfeld twist'' $F_D$ is explicitly constructed, as well as its inverse, and we investigate the complete QHSA associated with $Δ'$. We give a universal proof that the coassociator $Φ'=(S\otimes S\otimes S)Φ_{321}$ and canonical elements $α' = S(β),$ $β' = S(α)$ correspond to twisting the original coassociator $Φ= Φ_{123}$ and canonical elements $α,β$ with the Drinfeld twist $F_D$. Moreover in the quasi-triangular case, it is shown algebraically that the R-matrix $R' = (S\otimes S)R$ corresponds to twisting the original R-matrix $R$ with $F_D$. This has important consequences in knot theory, which will be investigated elsewhere.
dc.descriptionLatex file, 34 pages; typo corrections (in some formulae), minor changes and one reference added
dc.identifierhttps://arxiv.org/abs/math/9811062
dc.identifierhttp://arxiv.org/abs/math/9811062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77688
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleOn Quasi-Hopf superalgebras
dc.typetext

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