Hochschild homology and global dimension (09rit160)

Objectives

The objective of this proposal is to establish Han's conjecture
for a wider class of algebras. As mentioned under ``Overview", we,
Bergh and Madsen, have recently showed that the conjecture holds
for graded local algebras, Koszul algebras and graded cellular
algebras, provided the characteristic of the ground field is zero.
This cooperation began during the workshop ´´Hochschild Cohomology
of Algebras: Structure and Applications", held at BIRS in
September 2007. We are currently studying how Hochschild homology
behaves with respect to products in the category of finite
dimensional algebras, and intend to expand to short exact
sequences. Partial results obtained so far suggest that
establishing the conjecture for augmented algebras is now within
reach. This is our objective.

We are confident that a Research in Teams meeting at BIRS will be
productive and result in substantial progress towards our above
objective. Han's conjecture is ranked among the famous and
important problems in homological algebra. Establishing this
conjecture for augmented algebras would vastly broaden the
knowledge on the homological behavior of finite dimensional
algebras.