TY - JOUR
T1 - A Correspondence Between Homogeneous and Galois Coactions of Hopf Algebras
AU - De Commer, Kenny
AU - Konings, Johan
PY - 2019/5/1
Y1 - 2019/5/1
N2 - Let H be a Hopf algebra. A unital H-comodule algebra is called homogeneous if the algebra of coinvariants equals the ground field. A (not necessarily unital) H-comodule algebra is called Galois, or principal, or free, if the canonical map, also known as the Galois map, is bijective. In this paper, we establish a duality between a particular class of homogeneous H-comodule algebras, up to H-Morita equivalence, and a particular class of Galois H-comodule algebras, up to H-comodule algebra isomorphism.
AB - Let H be a Hopf algebra. A unital H-comodule algebra is called homogeneous if the algebra of coinvariants equals the ground field. A (not necessarily unital) H-comodule algebra is called Galois, or principal, or free, if the canonical map, also known as the Galois map, is bijective. In this paper, we establish a duality between a particular class of homogeneous H-comodule algebras, up to H-Morita equivalence, and a particular class of Galois H-comodule algebras, up to H-comodule algebra isomorphism.
KW - Equivariant Morita equivalence
KW - Galois actions
KW - Hopf algebras
UR - http://www.scopus.com/inward/record.url?scp=85065236915&partnerID=8YFLogxK
U2 - 10.1007/s10468-019-09892-6
DO - 10.1007/s10468-019-09892-6
M3 - Article
SN - 1386-923X
VL - 23
SP - 1387
EP - 1416
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 4
ER -