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• W2963255554 startingPage "867" @default.
• W2963255554 abstract "A laycle is the categorical analogue of a lazy cocycle. Twines (introduced by Bruguières) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If c is a braiding, the double braiding c2 is always a twine; we prove that it is a strong twine if and only if c satisfies a sort of modified braid relation (we call such c pseudosymmetric, as any symmetric braiding satisfies this relation). It is known that the category of Yetter–Drinfeld modules over a Hopf algebra H is symmetric if and only if H is trivial; we prove that the Yetter–Drinfeld category HYDH over a Hopf algebra H is pseudosymmetric if and only if H is commutative and cocommutative. We introduce as well the Hopf algebraic counterpart of pseudosymmetric braidings under the name pseudotriangular structures and prove that all quasitriangular structures on the 2n+1-dimensional pointed Hopf algebras E(n) are pseudotriangular. We observe that a laycle on a monoidal category induces a so-called pseudotwistor on every algebra in the category, and we obtain some general results (and give some examples) concerning pseudotwistors, inspired by the properties of laycles and twines." @default.
• W2963255554 created "2019-07-30" @default.
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• W2963255554 date "2010-06-01" @default.
• W2963255554 modified "2023-10-15" @default.
• W2963255554 title "Pseudosymmetric braidings, twines and twisted algebras" @default.
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• W2963255554 doi "https://doi.org/10.1016/j.jpaa.2009.08.008" @default.
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