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Title
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Pseudosymmetric braidings, twines and twisted algebras
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Author
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Abstract
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| 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 YetterDrinfeld modules over a Hopf algebra H is symmetric if and only if H is trivial; we prove that the YetterDrinfeld category View the MathML source 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. |
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Language
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English
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Source (journal)
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Journal of pure and applied algebra. - Amsterdam
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Publication
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Amsterdam
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2010
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ISSN
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0022-4049
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DOI
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10.1016/J.JPAA.2009.08.008
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Volume/pages
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214
:6
(2010)
, p. 867-884
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ISI
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000274928100014
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Full text (Publisher's DOI)
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