Algebra publication
Title
A relation between Hochschildt homology and cohomology for
Gorenstein rings
Author(s)
M. Van den Bergh.
Year
1996
Abstract
Let ``$HH$'' stand for Hochschildt (co)homology.
In this note we show that for many rings $A$ there exists $d\in\NN$
such that for an arbitrary $A$-bimodule $N$ we have $HH^i(N)=HH_{d-i}(N)
$.
Such a result may be viewed as
an analog of Poincare duality.
Combining this equality with a computation of Soergel allows one to
compute the Hochschildt homology of a regular minimal primitive
quotient of an enveloping algebra of a semisimple Lie algebra, answering
a question of Polo.
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