Title




Pseudosymmetric braidings, twines and twisted algebras


Author






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 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+1dimensional pointed Hopf algebras E(n) are pseudotriangular. We observe that a laycle on a monoidal category induces a socalled 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. 


Language




English


Source (journal)




Journal of pure and applied algebra.  Amsterdam


Publication




Amsterdam
:
2010


ISSN




00224049


Volume/pages




214
:6
(2010)
, p. 867884


ISI




000274928100014


Full text (Publisher's DOI)





