Crossed Products by Twisted Partial Actions: Separability, Semisimplicity, and Frobenius Properties

DOI10.1080/00927870802614764zbMath1200.16047OpenAlexW2085265092MaRDI QIDQ5305987

João Lazzarin, Dirceu Bagio, Antonio Paques

Publication date: 24 March 2010

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870802614764

zbMATH Keywords

crossed productsHopf algebrasrings of invariantssemisimple modulesFrobenius extensionsChevalley propertytwisted partial actionsseparable extensionssemisimple extensions

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Twisted and skew group rings, crossed products (16S35) Smash products of general Hopf actions (16S40) Hopf algebras and their applications (16T05)

Related Items

Partial Crossed Products and Goldie Rings ⋮ Twisted partial actions of Hopf algebras. ⋮ On the separability of the partial skew groupoid ring ⋮ Twisted partial coactions of Hopf algebras ⋮ Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras ⋮ A characterization of graded von Neumann regular rings with applications to Leavitt path algebras ⋮ Partial projective representations and partial actions. II. ⋮ Partial Groupoid Actions: Globalization, Morita Theory, and Galois Theory ⋮ When is a Crossed Product by a Twisted Partial Action Azumaya? ⋮ Recent developments around partial actions ⋮ Globalization of twisted partial actions ⋮ Epsilon-strongly graded rings, separability and semisimplicity ⋮ GALOIS CORRESPONDENCES FOR PARTIAL GALOIS AZUMAYA EXTENSIONS ⋮ On partial skew groupoid rings

Cites Work

• Unnamed Item
• Partial actions and Galois theory
• Partial actions and partial skew group rings.
• Crossed products by twisted partial actions and graded algebras.
• Modules, comodules, and cotensor products over Frobenius algebras
• Circle actions on \(C^*\)-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence
• On finite degree partial representations of groups.
• The structure of Frobenius algebras and separable algebras
• \(K\)-theory for partial crossed products by discrete groups
• Partial representations and partial group algebras
• On semisimple extensions and separable extensions over non commutative rings
• Separable algebras over commutative rings
• Globalizations of partial actions on nonunital rings
• Partial Skew Polynomial Rings: Prime and Maximal Ideals
• Partial (Co)Actions of Hopf Algebras and Partial Hopf-Galois Theory
• Partial Skew Polynomial Rings and Goldie Rings
• Partial actions of groups and actions of inverse semigroups
• PARTIAL ACTIONS OF GROUPS
• Associativity of crossed products by partial actions, enveloping actions and partial representations
• ISOMORPHISMS OF PARTIAL GROUP RINGS Research partially supported by CNPq Procs. 30111595-8 and 30024379-0 and FAPESP Proc. 00/07291-0.
• Actions of Inverse Semigroups on Algebras