Normal bases for Hopf-Galois algebras

Author:
H. F. Kreimer

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2853-2856

MSC (2000):
Primary 16W30

Published electronically:
March 14, 2002

MathSciNet review:
1908907

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Hopf algebra over a commutative ring such that is a finitely generated, projective module over , let be a right -comodule algebra, and let be the subalgebra of -coinvariant elements of . If is a Galois extension of and is a local subalgebra of the center of , then is a cleft right -comodule algebra or, equivalently, there is a normal basis for over .

**1.**Nicolas Bourbaki,*Elements of mathematics. Commutative algebra*, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR**0360549****2.**Yukio Doi and Mitsuhiro Takeuchi,*Cleft comodule algebras for a bialgebra*, Comm. Algebra**14**(1986), no. 5, 801–817. MR**834465**, 10.1080/00927878608823337**3.**H. F. Kreimer and P. M. Cook II,*Galois theories and normal bases*, J. Algebra**43**(1976), no. 1, 115–121. MR**0424782****4.**H. F. Kreimer and M. Takeuchi,*Hopf algebras and Galois extensions of an algebra*, Indiana Univ. Math. J.**30**(1981), no. 5, 675–692. MR**625597**, 10.1512/iumj.1981.30.30052**5.**Dmitriy Rumynin,*Hopf-Galois extensions with central invariants and their geometric properties*, Algebr. Represent. Theory**1**(1998), no. 4, 353–381. MR**1683618**, 10.1023/A:1009944607078

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
16W30

Retrieve articles in all journals with MSC (2000): 16W30

Additional Information

**H. F. Kreimer**

Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510

Email:
kreimer@math.fsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06442-0

Keywords:
Cleft Hopf algebra,
normal basis

Received by editor(s):
April 11, 2001

Received by editor(s) in revised form:
May 23, 2001

Published electronically:
March 14, 2002

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2002
American Mathematical Society