Strong group coalgebras
S. Caenepeel, K. Janssen
TL;DR
This paper introduces the concept of strong group coalgebras, generalizing strongly graded coalgebras, and explores their properties and special types like cleft and smash coproduct group coalgebras.
Contribution
It defines strong group coalgebras, provides characterizations, and studies specific subclasses such as cleft and smash coproduct group coalgebras.
Findings
Characterizations of strong group coalgebras
Descriptions of cleft and smash coproduct group coalgebras
Framework for analyzing generalized graded coalgebras
Abstract
We introduce strong group coalgebras, as a generalization of strongly graded coalgebras. We give several characterizations, and study two special types of strong group coalgebras, namely cleft group algebras (or crossed coproduct group coalgebras) and smash coproduct group coalgebras.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Rings, Modules, and Algebras