|
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)
|
|
|
|
|
|