Publication
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+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.
Language
English
Source (journal)
Journal of pure and applied algebra. - Amsterdam
Publication
Amsterdam : 2010
ISSN
0022-4049
Volume/pages
214:6(2010), p. 867-884
ISI
000274928100014
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 14.04.2010
Last edited 20.06.2017
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