Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Cotensor products of modules

Author(s): L. Abrams; C. Weibel
Journal: Trans. Amer. Math. Soc. 354 (2002), 2173-2185.
MSC (2000): Primary 16E30; Secondary 16W30, 16E40
Posted: February 1, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $C$ be a coalgebra over a field $k$ and $A$ its dual algebra. The category of $C$-comodules is equivalent to a category of $A$-modules. We use this to interpret the cotensor product $M \square N$ of two comodules in terms of the appropriate Hochschild cohomology of the $A$-bimodule $M \otimes N$, when $A$ is finite-dimensional, profinite, graded or differential-graded. The main applications are to Galois cohomology, comodules over the Steenrod algebra, and the homology of induced fibrations.

References:

[Abr]
L. ABRAMS, ``Modules, Comodules and Cotensor Product over Frobenius Algebras,'' J. Algebra 219 (1999), 201-213. MR 2001b:16038

[AF]
F. ANDERSON AND K. FULLER, Rings and Categories of Modules, Springer Verlag, 1974. MR 54:5281

[Br]
A. BRUMER, ``Pseudocompact algebras, profinite groups and class formations,'' J. Algebra 4 (1966), 442-470. MR 34:2650

[Car]
P. CARTIER, ``Cohomology des coalgèbres (Exposés 4,5),'' In Séminaire Sophus Lie, 1955-56, Faculté des Sciences de Paris, 1957.
[CE]
H. CARTAN AND S. EILENBERG, Homological Algebra, Princeton University Press, 1956. MR 17:1040e

[Doi]
Y. DOI, ``Homological Coalgebra,'' J. Math Soc. Japan 33, no. 1 (1981), 31-50. MR 82g:16014

[EM]
S. EILENBERG AND J. MOORE, ``Homology and fibrations I: Coalgebras, cotensor product and its derived functors,'' Comm. Math. Helv. 40 (1966), 199-236. MR 34:3579

[Fog]
J. FOGARTY, Invariant Theory, Benjamin, 1969. MR 39:1458

[Mac]
S. MACLANE, Homology, Springer Verlag, 1963. MR 28:122

[MM]
J. MILNOR AND J. MOORE, ``On the structure of Hopf algebras,'' Annals of Math. (2) 81 (1965), 211-264. MR 30:4259

[Rad]
D. RADFORD, ``Coreflexive coalgebras,'' J. Algebra 26 (1973), 512-535. MR 46:6160

[Rav]
D. C. RAVENEL, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986. MR 87j:55003

[Sw]
M. SWEEDLER, Hopf Algebras, Benjamin, 1969. MR 40:5705

[T]
E. J. TAFT, ``Reflexivity of algebras and coalgebras,'' Amer. J. Math. 94 (1972), 1111-1130. MR 46:9095

[Wei]
C. WEIBEL, An Introduction to Homological Algebra, Cambridge Studies in Adv. Math. 38, Cambridge Univ. Press, 1994. MR 95f:18001

[Wit]
L. WITKOWSKI, ``On coalgebras and linearly topological rings,'' Colloquium Mathematicum 40 Fasc. 2 (1979), 207-218. MR 81c:16057

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 16E30, 16W30, 16E40

Retrieve articles in all Journals with MSC (2000): 16E30, 16W30, 16E40

Additional Information:

L. Abrams
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication: Department of Mathematics, George Washington University, Washington, D.C. 20052
Email: labrams@gwu.edu

C. Weibel
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: weibel@math.rutgers.edu

DOI: 10.1090/S0002-9947-02-02883-0
PII: S 0002-9947(02)02883-0
Received by editor(s): April 18, 2000
Received by editor(s) in revised form: June 14, 2001
Posted: February 1, 2002
Additional Notes: The second author was partially supported by NSF grants.
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google