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HOCHSCHILD HOMOLOGY CRITERIA FOR SMOOTHNESS Luchezar L. Avramov and Micheline Vigu e-Poirrier
 

Summary: HOCHSCHILD HOMOLOGY CRITERIA FOR SMOOTHNESS
Luchezar L. Avramov and Micheline Vigu e-Poirrier
Introduction
When R is a commutative algebra over a eld k, its Hochschild homology can be
de ned by the formula
HH  (R) = Tor
R
R
 (R; R);
where the tensor product is over k, and R is viewed as an
R
R-module via
the multiplication map  :
R
R ! R, (a
0
a 00 ) = a 0 a 00 . The t-product of
Cartan-Eilenberg, cf. [CE, Chapter XI], provides HH  (R) with a structure of skew-
commutative (also called graded-commutative) graded algebra over HH 0 (R) = R.
As HH 1 (R) is canonically identi ed

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics