Аннотация:
In this paper, we first introduce the notion of the
$\pi$-pivotal elements in a weak
Turaev
$\pi$-coalgebra
$H$
and show that the representation category of
$H$
is a pivotal crossed category if and only
if there is a
$\pi$-pivotal element in
$H$.
Also we discuss the relation between
$\pi$-pivotal elements and
$\pi$-ribbon elements of
a quasitriangular weak Turaev
$\pi$-coalgebra.
Finally, we obtain a generalized Deligne Type theorem.
Ключевые слова:pivotal crossed group category, weak Turaev
$\pi$-coalgebra, ribbon crossed group
category.
