André-Quillen homology via functor homology
Author:
Teimuraz Pirashvili
Journal:
Proc. Amer. Math. Soc. 131 (2003), 1687-1694
MSC (2000):
Primary 13D03, 18G25
DOI:
https://doi.org/10.1090/S0002-9939-02-06741-2
Published electronically:
October 1, 2002
MathSciNet review:
1955254
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We obtain André-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed sets.
- 1.
A. K. BOUSFIELD and E.M. FRIEDLANDER. Homotopy theory of
-spaces, spectra, and bisimplicial sets. Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, pp. 80-130, Lecture Notes in Math., 658, Springer, 1978. MR 80e:55021
- 2. A. DOLD and D. PUPPE. Homologie nicht-additiver Funktoren, Anwendungen. Ann. Inst. Fourier 11 (1961), 201-312. MR 27:186
- 3. J. - L. LODAY. Opérations sur l'homologie cyclique des algèbres commutatives. Invent. Math. 96 (1989), 205-230. MR 89m:18017
- 4. S. MAC LANE. Homology. Classics in Mathematics. Springer-Verlag, Berlin, 1995. x+422 pp. MR 96d:18001
- 5. T. PIRASHVILI. Hodge decomposition of higher order Hochschild homology. Ann. Sci. École Norm. Sup. (4) 33 (2000), no. 2, 151-179. MR 2001e:19006
- 6.
T. PIRASHVILI. Dold-Kan type theorem for
-groups. Math. Ann. 318 (2000), no. 2, 277-298. MR 2001i:20112
- 7. T. PIRASHVILI and B. RICHTER. Robinson-Whitehouse complex and stable homotopy. Topology 39 (2000), no. 3, 525-530. MR 2001e:13019
- 8. D.G. QUILLEN. On the (co)homology of commutative rings. AMS Proc. Sym. Pure Math. 17 (1970), 65-87. MR 41:1722
- 9. G. SEGAL. Categories and cohomology theories. Topology 13 (1974), 293-312. MR 50:5782
- 10. S. A. WHITEHOUSE. Gamma (co)homology of commutative algebras and some related representations of the symmetric group. Thesis. University of Warwick. 1994.
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13D03, 18G25
Retrieve articles in all journals with MSC (2000): 13D03, 18G25
Additional Information
Teimuraz Pirashvili
Affiliation:
Razmadze Mathematical Institute, Rukhadze str. 1, Tbilisi 380093, Republic of Georgia
Email:
pira@rmi.acnet.ge
DOI:
https://doi.org/10.1090/S0002-9939-02-06741-2
Received by editor(s):
October 13, 2001
Received by editor(s) in revised form:
January 17, 2002
Published electronically:
October 1, 2002
Additional Notes:
The author was partially supported by the grant INTAS-99-00817 and by the TMR network K-theory and algebraic groups, ERB FMRX CT-97-0107
Communicated by:
Paul Goerss
Article copyright:
© Copyright 2002
American Mathematical Society