Hochschild Cohomology and Koszul Algebras


Ragnar Buchweitz

University of Toronto

Northeastern University

Thursday, March 25, 2004


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   Hochschild cohomology is an important, yet poorly understood invariant of an algebra. In particular, it is explicitly known only in a few cases. The main result here shows that Hochschild cohomology behaves well with respect to Koszul duality. We use this to determine the Hochschild cohomology of some classical varieties, such as those of minimal degree, and of some quantum affine spaces and Artin-Schelter algebras. As a consequence we show (joint with Green, Madsen, Solberg) that there are artinian algebras that have only finitely many nonzero Hochschild cohomology groups but are of infinite global dimension, answering negatively an old question by Happel.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Maxim Braverman.

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Posted: March 17, 2004    URL: