|
Geometry & Topology Monographs 16
(2009) 367–400
|
| 1 |
E Abe, Hopf
algebras, Cambridge Tracts in Math. 74, Cambridge Univ.
Press (1980) MR594432
Translated from the Japanese by H Kinoshita and
H Tanaka |
| 2 |
J Bichon, The representation
category of the quantum group of a nondegenerate bilinear
form, Comm. Algebra 31 (2003) 4831–4851 MR1998031 |
| 3 |
R J Blattner,
S Montgomery, Crossed
products and Galois extensions of Hopf algebras,
Pacific J. Math. 137 (1989) 37–54 MR983327 |
| 4 |
S U Chase,
D K Harrison, A Rosenberg, Galois theory
and Galois cohomology of commutative rings, Mem. Amer.
Math. Soc. No. 52 (1965) 15–33 MR0195922 |
| 5 |
S U Chase,
M E Sweedler, Hopf algebras and Galois
theory, Lecture Notes in Math. 97, Springer (1969) MR0260724 |
| 6 |
M Cohen, D
Fischman, S Montgomery, Hopf Galois
extensions, smash products, and Morita equivalence, J.
Algebra 133 (1990) 351–372 MR1067411 |
| 7 |
Y Doi, M
Takeuchi, Cleft comodule algebras for a bialgebra,
Comm. Algebra 14 (1986) 801–817 MR834465 |
| 8 |
Y Doi, M
Takeuchi, Hopf–Galois
extensions of algebras, the Miyashita–Ulbrich action, and
Azumaya algebras, J. Algebra 121 (1989) 488–516
MR992778 |
| 9 |
V G
Drinfel″d, Almost cocommutative Hopf algebras,
Algebra i Analiz 1 (1989) 30–46 MR1025154 |
| 10 |
C Greither, B
Pareigis, Hopf Galois
theory for separable field extensions, J. Algebra 106
(1987) 239–258 MR878476 |
| 11 |
R Günther,
Crossed products
for pointed Hopf algebras, Comm. Algebra 27 (1999)
4389–4410 MR1705876 |
| 12 |
C Kassel, Quantum
groups, Graduate Texts in Math. 155, Springer (1995)
MR1321145 |
| 13 |
H F Kreimer, M
Takeuchi, Hopf algebras
and Galois extensions of an algebra, Indiana Univ.
Math. J. 30 (1981) 675–692 MR625597 |
| 14 |
R G Larson,
M E Sweedler, An associative orthogonal
bilinear form for Hopf algebras, Amer. J. Math. 91
(1969) 75–94 MR0240169 |
| 15 |
G Letzter, Coideal
subalgebras and quantum symmetric pairs, from: "New
directions in Hopf algebras" (editors S Montgomery, H J
Schneider), Math. Sci. Res. Inst. Publ. 43, Cambridge Univ.
Press (2002) 117–165 MR1913438 |
| 16 |
A Masuoka, Cleft extensions
for a Hopf algebra generated by a nearly primitive
element, Comm. Algebra 22 (1994) 4537–4559
MR1284344 |
| 17 |
A Masuoka, T
Yanai, Hopf module
duality applied to X–outer Galois theory, J.
Algebra 265 (2003) 229–246 MR1984909 |
| 18 |
J C McConnell,
J C Robson, Noncommutative Noetherian rings,
Graduate Studies in Math. 30, Amer. Math. Soc. (2001) MR1811901
With the cooperation of L W Small |
| 19 |
A Milinski,
Actions
of pointed Hopf algebras on prime algebras, Comm.
Algebra 23 (1995) 313–333 MR1311791 |
| 20 |
S Montgomery, Hopf
algebras and their actions on rings, CBMS Regional
Conference Series in Math. 82, Conference Board of the Math.
Sciences (1993) MR1243637 |
| 21 |
S Montgomery,
D S Passman, Outer Galois theory of prime
rings, Rocky Mountain J. Math. 14 (1984) 305–318
MR747279 |
| 22 |
S Montgomery,
H J Schneider, Prime ideals in Hopf
Galois extensions, Israel J. Math. 112 (1999)
187–235 MR1715517 |
| 23 |
S H Ng,
Nonsemisimple
Hopf algebras of dimension p2, J. Algebra
255 (2002) 182–197 MR1935042 |
| 24 |
B Pareigis, Forms
of Hopf algebras and Galois theory, from: "Topics in
algebra, Part 1 (Warsaw, 1988)" (editors S Balcerzyk, T
Józefiak, J Krempa, D Simson, W Vogel), Banach Center
Publ. 26, PWN (1990) 75–93 MR1171227 |
| 25 |
P Schauenburg,
Hopf
bi-Galois extensions, Comm. Algebra 24 (1996)
3797–3825 MR1408508 |
| 26 |
P Schauenburg,
Galois
correspondences for Hopf bi-Galois extensions, J.
Algebra 201 (1998) 53–70 MR1608691 |
| 27 |
P Schauenburg,
Galois
objects over generalized Drinfeld doubles, with an application
to uq(sl2), J. Algebra 217
(1999) 584–598 MR1700516 |
| 28 |
P Schauenburg,
Bi-Galois
objects over the Taft algebras, Israel J. Math. 115
(2000) 101–123 MR1749674 |
| 29 |
P Schauenburg,
Hopf–Galois and bi-Galois extensions, from:
"Galois theory, Hopf algebras, and semiabelian categories"
(editors G Janelidze, B Pareigis, W Tholen), Fields Inst.
Commun. 43, Amer. Math. Soc. (2004) 469–515 MR2075600 |
| 30 |
P Schauenburg,
H J Schneider, Galois type extensions and Hopf
algebras, to appear in the Proceedings of the 2001 Warsaw
Conference |
| 31 |
H J Schneider,
Principal
homogeneous spaces for arbitrary Hopf algebras, Israel
J. Math. 72 (1990) 167–195 MR1098988 |
| 32 |
H J Schneider,
Normal basis
and transitivity of crossed products for Hopf algebras,
J. Algebra 152 (1992) 289–312 MR1194305 |
| 33 |
M E Sweedler,
Cohomology of
algebras over Hopf algebras, Trans. Amer. Math. Soc.
133 (1968) 205–239 MR0224684 |
| 34 |
M E Sweedler,
Hopf algebras, Math. Lecture Note Ser., W. A. Benjamin
(1969) MR0252485 |
| 35 |
E J Taft, The
order of the antipode of finite-dimensional Hopf algebra,
Proc. Nat. Acad. Sci. U.S.A. 68 (1971) 2631–2633 MR0286868 |
| 36 |
M Takeuchi, Morita
theorems for categories of comodules, J. Fac. Sci. Univ.
Tokyo Sect. IA Math. 24 (1977) 629–644 MR0472967 |
| 37 |
K H Ulbrich,
Galoiserweiterungen
von nichtkommutativen Ringen, Comm. Algebra 10 (1982)
655–672 MR647213 |
| 38 |
F Van Oystaeyen, Y
Zhang, Galois-type
correspondences for Hopf-Galois extensions, from:
"Proceedings of Conference on Algebraic Geometry and Ring
Theory in honor of Michael Artin, Part III (Antwerp, 1992)",
K–Theory 8 (1994) 257–269 MR1291021 |
| 39 |
S Westreich,
A
Galois-type correspondence theory for actions of
finite-dimensional pointed Hopf algebras on prime
algebras, J. Algebra 219 (1999) 606–624 MR1706837 |
| 40 |
S Westreich, T
Yanai, More about a
Galois-type correspondence theory, J. Algebra 246
(2001) 629–640 MR1872117 |
| 41 |
T Yanai, Correspondence
theory of Kharchenko and X–outer actions of pointed Hopf
algebras, Comm. Algebra 25 (1997) 1713–1740
MR1446125 |
