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2016

Hopf algebroids, Hopf categories and their Galois theories

Canlubo, Clarisson Rizzie

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Understand

Hopf algebroids are generalization of Hopf algebras over non-commutative base rings.

It consists of a left- and a right-bialgebroid structure related by a map called the antipode.
However, if the base ring of a Hopf algebroid is commutative one does not necessarily have a Hopf algebra.
Meanwhile, a Hopf category is the categorification of a Hopf algebra.

Hopf algebroids, Hopf categories and their Galois theories · Around

Built on

P. Schauenburg. A bialgebra that admits a Hopf-Galois extension is a Hopf algebra
1997
Earlier work this paper cites.
A. Connes and H. Moscovici. Cyclic cohomology and Hopf algebras
1999
Earlier work this paper cites.

Similar

J. M. Garcia-Bondia and J. C. Várilly and H. Figueroa. Elements of Noncommutative Geometry
2001
Cited alongside, same era.
E. Batista and S. Caenepeel and J. Vercruysse. Hopf categories
2004
Cited alongside, same era.

Then

G. Böhm and K. Szlachányi. Hopf algebroids with bijective antipodes: axioms, integrals, and duals
2004
Later among the works it cites.
G. Böhm. Hopf Algebroids
2009
Later among the works it cites.

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