Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


References [Enhancements On Off] (What's this?)

  • 1. A. K. BOUSFIELD and E.M. FRIEDLANDER. Homotopy theory of $\Gamma $-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 $\Gamma$-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: 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

American Mathematical Society