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)

 
 

 

Splittings of Hochschild's complex for commutative algebras


Author: Patrick J. Fleury
Journal: Proc. Amer. Math. Soc. 30 (1971), 405-411
MSC: Primary 18H20
DOI: https://doi.org/10.1090/S0002-9939-1971-0291252-1
MathSciNet review: 0291252
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Barr has shown that one may split Hochschild's complex for commutative algebras into Harrison's complex plus a shuffle subcomplex when working over a field of characteristic zero. We construct a splitting here for the above complex over a ring containing a field which does not have characteristic two and this splitting has Barr's splitting as a special case.


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

  • [1] M. Barr, Harrison homology, Hochschild homology and triples, J. Algebra 8 (1968), 314-323. MR 36 #3851. MR 0220799 (36:3851)
  • [2] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [3] S. Eilenberg and S. Mac Lane, On the groups $ H(\pi ,n)$. I, Ann. of Math. (2) 58 (1953), 55-106. MR 15, 54. MR 0056295 (15:54b)
  • [4] P. Fleury, Aspects of Harrison's homology theory, Dissertation, University of Illinois, Urbana, Ill., 1970.
  • [5] D. K. Harrison, Commutative algebras and cohomology, Trans. Amer. Math. Soc. 104 (1962), 191-204. MR 26 #176. MR 0142607 (26:176)
  • [6] I. Herstein, Noncommutative rings, Carus Math. Monographs, no. 15, Math. Assoc. Amer.; distributed by Wiley, New York, 1968. MR 37 #2790. MR 0227205 (37:2790)
  • [7] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 18H20

Retrieve articles in all journals with MSC: 18H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0291252-1
Keywords: Shuffle, Harrison homology theory, Hochschild homology theory, splitting, differential graded algebra
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society