Picard groups for graded coalgebras (original) (raw)
2000, Communications in Algebra
AI-generated Abstract
This paper introduces group invariants for graded coalgebras, specifically focusing on the category of graded comodules. It establishes that the category of graded comodules over a G-graded coalgebra is isomorphic to that over the smash coproduct with a group algebra. The notion of graded equivalence is introduced, leading to the construction of a graded Picard group that characterizes these equivalences. The study also applies Morita-Takeuchi theory to derive new examples of the standard Picard group of coalgebras.
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