Morita theory for corings and cleft entwining structures

By Stefaan Caenepeel, Joost Vercruysse, Shuanhong Wang. 2002

52 citations recorded by the source corpus.

Abstract Using the theory of corings, we generalize and unify Morita contexts introduced by Chase and Sweedler [Hopf Algebras and Galois Theory, in: Lecture Notes in Math., vol. 97, Springer-Verlag, Berlin, 1969], Doi [Generalized smash products and Morita contexts for arbitrary Hopf algebras, in: J. Bergen, S. Montgomery (Eds.), Advances in Hopf algebras, in: Lecture Notes in Pure and Appl. Math., vol. 158, Dekker, New York, 1994], and Cohen, Fischman, and Montgomery [J. Algebra 133 (1990) 351]. We discuss when the contexts are strict. We apply our theory to corings arising from entwining structures, and this leads us to the notion of cleft entwining structure.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0a7e285d900e821030f1d1f566d8e634250e464f

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Citations in the corpus

Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings (2002, unknown): “The relationship between Noncommutative Descent Theory and Galois corings with grouplike is known (see [4] and [ 7 ]).”
Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties (2004, methodology): “This has been clarified in [ 16 ], using the notion of Frobenius coring.”
Partial (Co)Actions of Hopf Algebras and Partial Hopf-Galois Theory (2006, methodology): “It follows from [ 9, Theorem 2.7 ] that Q ∼ A as k-modules.”