Partial actions of weak Hopf algebras: smash product, globalization and Morita theory.

DOI10.1016/j.jpaa.2015.05.031zbMath1331.16024arXiv1409.0232OpenAlexW1606840874MaRDI QIDQ494110

Glauber Quadros, Felipe Castro, Antonio Paques, Alveri Sant'Ana

Publication date: 31 August 2015

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.0232

zbMATH Keywords

weak Hopf algebrasMorita contextssmash productspartial actionsglobalizations

Mathematics Subject Classification ID

Smash products of general Hopf actions (16S40) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Hopf algebras and their applications (16T05)

Related Items (12)

Partial actions of weak Hopf algebras on coalgebras ⋮ Morita, Galois, and the trace map: a survey ⋮ Globalization of partial group actions on semiprime Lie algebras and unital Jordan algebras ⋮ Geometric partial comodules over flat coalgebras in abelian categories are globalizable ⋮ Partial Hopf-Galois theory ⋮ Partial actions of a Hopf algebra on its base field and the corresponding partial smash product algebra ⋮ A (partial) weak smash coproduct ⋮ Recent developments around partial actions ⋮ Partial actions of \(C^{*}\)-quantum groups ⋮ Globalization of partial cohomology of groups ⋮ Hopf algebras arising from partial (co)actions ⋮ Partial (co)actions of Taft and Nichols Hopf algebras on their base fields

Cites Work

• Circle actions on \(C^*\)-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence
• Enveloping actions and Takai duality for partial actions.
• Weak Hopf algebras. I: Integral theory and \(C^*\)-structure
• A coassociative \(C^*\)-quantum group with nonintegral dimensions
• Globalization theorems for partial Hopf (co)actions, and some of their applications
• Enveloping Actions for Partial Hopf Actions
• Partial (Co)Actions of Hopf Algebras and Partial Hopf-Galois Theory
• Associativity of crossed products by partial actions, enveloping actions and partial representations
• Partial Groupoid Actions: Globalization, Morita Theory, and Galois Theory
• Duality for Groupoid (Co)Actions
• Separable Groupoid Rings
• Weak Hopf algebras. II: Representation theory, dimensions, and the Markov trace
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