|
André-Quillen homology via functor homology
Author:
Teimuraz Pirashvili
Journal:
Proc. Amer. Math. Soc. 131 (2003), 1687-1694
MSC (2000):
Primary 13D03, 18G25
Posted:
October 1, 2002
MathSciNet review:
1955254
Full-text PDF Free Access
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 Γ-spaces, spectra, and
bisimplicial sets, Geometric applications of homotopy theory (Proc.
Conf., Evanston, Ill., 1977), II, Lecture Notes in Math., vol. 658,
Springer, Berlin, 1978, pp. 80–130. MR 513569
(80e:55021)
- 2.
Albrecht
Dold and Dieter
Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann.
Inst. Fourier Grenoble 11 (1961), 201–312 (German,
with French summary). MR 0150183
(27 #186)
- 3.
Jean-Louis
Loday, Opérations sur l’homologie cyclique des
algèbres commutatives, Invent. Math. 96
(1989), no. 1, 205–230 (French). MR 981743
(89m:18017), http://dx.doi.org/10.1007/BF01393976
- 4.
Saunders
Mac Lane, Homology, Classics in Mathematics, Springer-Verlag,
Berlin, 1995. Reprint of the 1975 edition. MR 1344215
(96d:18001)
- 5.
Teimuraz
Pirashvili, Hodge decomposition for higher order Hochschild
homology, Ann. Sci. École Norm. Sup. (4) 33
(2000), no. 2, 151–179 (English, with English and French
summaries). MR
1755114 (2001e:19006), http://dx.doi.org/10.1016/S0012-9593(00)00107-5
- 6.
Teimuraz
Pirashvili, Dold-Kan type theorem for Γ-groups, Math.
Ann. 318 (2000), no. 2, 277–298. MR 1795563
(2001i:20112), http://dx.doi.org/10.1007/s002080000120
- 7.
T.
Pirashvili and B.
Richter, Robinson-Whitehouse complex and stable homotopy,
Topology 39 (2000), no. 3, 525–530. MR 1746906
(2001e:13019), http://dx.doi.org/10.1016/S0040-9383(99)00014-2
- 8.
Daniel
Quillen, On the (co-) homology of commutative rings,
Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII,
New York, 1968), Amer. Math. Soc., Providence, R.I., 1970,
pp. 65–87. MR 0257068
(41 #1722)
- 9.
Graeme
Segal, Categories and cohomology theories, Topology
13 (1974), 293–312. MR 0353298
(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.
- 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.
Similar Articles
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:
http://dx.doi.org/10.1090/S0002-9939-02-06741-2
PII:
S 0002-9939(02)06741-2
Received by editor(s):
October 13, 2001
Received by editor(s) in revised form:
January 17, 2002
Posted:
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
|
