Yetter-Drinfeld π-modules over weak T-coalgebras

Abstract

In this paper we introduce the notion of a weak Yetter-Drinfeld group module over a weak T-coalgebra and give some basic properties. Moreover we also prove that the category of weak Yetter-Drinfeld group modules is isomorphic to the center of the representation category of a weak T-coalgebra H denoted by Z (Rep(H)).

The Morita contexts and galois extensions for weak Hopf group coalgebras

“…Directly from the equity (11) B is an algebra and from Eq. (16) in [11] it is also a weak right H l H rπ-comodulelike algebra. We define λ α :…”

“…The axioms are the same as ones for Hopf algebras, but the multiplicativity of the counit and comultiplicativity of the unit are replaced by weaker axioms. These naturally lead to the introduction of weak Hopf algebras in Turaev module category called weak Hopf group coalgebras in [9][10][11][12].…”

“…The first parts of (18)-(21) are obtained in the following way. Applying x ⊗ y ∈ H i ⊗ H i to both sides of them, we get: [11] = f (( [11] = f ((xy) [11] = f (( [11] = ε(…”

“…To prove the statement (1) we firstly claim that the above actions are reasonable. In fact, for any [11] =…”

“…Secondly we prove that A exactly is a left and right A H * -module. In fact, for any a, b, c [11] = f (S −1…”