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DERIVED INVARIANCE OF HIGHER STRUCTURES ON THE HOCHSCHILD COMPLEX

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Bernhard Keller

We show that derived equivalences preserve the homotopy type of the
(cohomological) Hochschild complex as a B-infinity algebra. More
generally, we prove that, as an object of the homotopy category of
B-infinity algebras, the Hochschild complex is contravariant with
respect to fully faithful derived tensor functors. We also show that
the Hochschild complexes of a Koszul algebra and its dual are homotopy
equivalent as B-infinity algebras. In particular, their Hochschild
cohomologies are isomorphic as algebras, which is a recent result by
R.-O. Buchweitz, and as Lie algebras. Our methods also yield a
derived invariant definition of the Hochschild complex of an exact
category.

http://www.math.jussieu.fr/~keller/publ/dihabs.html

Bernhard Keller, le 6 octobre, 2003.

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