Homology and cohomology with coefficients, of an algebra over a quadratic operad

Journal of Pure and Applied Algebra

Volumn 132, Issue 3, 1998, Pages 221-258

  Balavoine, David ^a  

^a UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032553255     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(97)00131-X     Document Type: Article

References (22)

1. [1] D. Balavoine, Deformation of algebras over a quadratic operad, in: J.-L. Loday, J. Stasheff, A.A. Voronov (Eds.), Operads: Proc. Renaissance Conf., Contemp. Math., vol. 202, AMS, Providence, RI, 1997, pp. 207-234.
2. [2] M. Barr, Cartan-Einlenberg cohomology and triples, J. Pure Appl. Algebra 112 (1996) 219-238
3. [3] M. Barr, J. Beck, Homology and standart construction theory, in: Seminar on Triples and Categorical Homology, Lecture Notes in Mathematics, vol. 80, Springer, Berlin, 1969, pp. 245-335
4. [4] H. Cartan, S. Eilenberg, Homological Algebra, Princeton University Press, Princeton, NJ, 1956.
5. [5] T. Fox, An introduction to algebraic deformation theory, J. Pure Appl. Algebra 84 (1993) 17-41.
6. [6] T. Fox, M. Markl, Distributive laws, bialgebras and cohomology, in: J.-L. Loday, J. Stasheff, A.A. Voronov (Eds.), Operads: Proc. Renaissance Conf., Contemp. Math., vol. 202, AMS, Providence, RI, 1997, pp. 167-205.
7. [7] M. Gerstenhaber, The cohomology structure of an associative ring, Ann. Math. 78 (1963) 267-288.
8. [8] M. Gerstenhaber, On the deformation of rings and algebras, Ann. Math. 79 (1964) 59-103.
9. [9] M. Gerstenhaber, S.D. Schack, Algebras, bialgebras, quantum groups and algebraic deformations, in: M. Gerstenhaber, J. Stasheff (Eds.), Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Amherst, MA, 1990, Contemp. Math., vol. 134, AMS, Providence, RI, 1992, pp. 51-92.
10. [9] M. Gerstenhaber, S.D. Schack, Algebras, bialgebras, quantum groups and algebraic deformations, in: M. Gerstenhaber, J. Stasheff (Eds.), Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Amherst, MA, 1990, Contemp. Math., vol. 134, AMS, Providence, RI, 1992, pp. 51-92.
11. [10] E. Getzler, J.D.S. Jones, Operads, homotopy algebra and iterated integrals for double loop space (1994) preprint hep-th/9403055.
12. [11] V. Ginzburg, M.M. Kapranov, Koszul duality for operads, Duke J. Math. 76 (1) (1994) 203-272.
13. [12] D.K. Harrison, Commutative algebras and cohomology, Trans. AMS 104 (1962) 191-204.
14. [13] T. Kimura, A.A. Voronov, The cohomology of algebras over moduli spaces, in: R. Dijkgraaf, C. Faber, G. Van Der Geer (Eds.), The Moduli Space of Curves, Progress in Mathematics, vol. 129, Birkhauser, Boston, MA, 1995, pp. 305-334.
15. [14] M. Livernet, private communication.
16. [15] J.-L. Loday, Une version non commutative des algèbres de Lie: les algèbres de Leibniz, L'Ens. Math. 39 (1993) 269-293.
17. [16] J.-L. Loday, La renaissance des opérades, Séminaire Bourbaki exposé n° 792, Novembre 1994, Astérisque 237 (1996) 47-74.
18. [17] J.-L. Loday, Cup-product for Leibniz cohomology and dual Leibniz algebras, Math. Scand. 77 (1995) 189-196.
19. [18] J.-L. Loday, T. Pirashvili, Universal envelopping algebra of Leibniz Algebra and (co) homology, Math. Annal. 296 (1993) 139-158.
20. [19] M. Markl, Models for operads, Comm. Algebra 24 (4) (1996) 1471-1500.
21. [20] S. Mac Lane, Categories for the Working Mathematician, Springer, Berlin, 1971.
22. [21] J.-P. May, Geometry of iterated loop spaces, Lecture Notes in Mathematics, vol. 271, Springer, Berlin, 1972.