Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the vanishing of homology and cohomology groups of associative algebras


Author: Rolf Farnsteiner
Journal: Trans. Amer. Math. Soc. 306 (1988), 651-665
MSC: Primary 16A61; Secondary 17B56
DOI: https://doi.org/10.1090/S0002-9947-1988-0933311-0
MathSciNet review: 933311
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper establishes sufficient conditions for the vanishing of the homology and cohomology groups of an associative algebra with coefficients in a two-sided module.


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

  • [1] D. W. Barnes, On the cohomology of soluble Lie algebras, Math. Z. 101 (1967), 343-349. MR 0220784 (36:3836)
  • [2] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 0077480 (17:1040e)
  • [3] C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124. MR 0024908 (9:567a)
  • [4] J. Dixmier, Cohomologie des algèbres de Lie nilpotentes, Acta Math. (Szeged) 16 (1955), 246-250. MR 0074780 (17:645b)
  • [5] A. S. Dzhumadil'daev, On the cohomology of modular Lie algebras, Math. USSR Sb. 47(1) (1984), 127-143.
  • [6] R. Farnsteiner, On the cohomology of associative algebras and Lie algebras, Proc. Amer. Math. Soc. 99 (1987), 415-420. MR 875373 (88d:17015)
  • [7] A. Guichardet, Cohomologie des groupes topologiques et des algèbres de Lie, Cedic/Fernand Nathan, Paris, 1980. MR 644979 (83f:22004)
  • [8] G. P. Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. (2) 46 (1945), 58-67. MR 0011076 (6:114f)
  • [9] -, On the cohomology theory for associative algebras, Ann. of Math. (2) 47 (1946), 568-579. MR 0016762 (8:64c)
  • [10] N. Jacobson, Lie algebras, Dover, New York, 1979. MR 559927 (80k:17001)
  • [11] H. Strade and R. Farnsteiner, Modular Lie algebras and their representations, Dekker, New York, 1988. MR 929682 (89h:17021)
  • [12] J. H. C. Whitehead, On the decomposition of an infinitesimal group, Proc. Cambridge Philos. Soc. 32 (1936), 229-237.
  • [13] -, Certain equations in the algebra of a semi-simple infinitesimal group, Quart. J. Math. 8 (1937), 220-237.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A61, 17B56

Retrieve articles in all journals with MSC: 16A61, 17B56


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0933311-0
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society