Hochschild homology / cohomology of preprojective algebras of ADET quivers

Preprojective algebras [Pi]q of quivers Q were introduced by Gelfand and Ponomarev in 1979 in order to provide a model for quiver representations (in the special case of finite Dynkin quivers). They showed that in the Dynkin case, the preprojective algebra decomposes as the direct sum of all indecomposable representations of the quiver with multiplicity 1. Since then, preprojective algebras have found many other important applications, see e.g. to Kleinian singularities. In this thesis, I computed the Hochschild homology/cohomology of [Pi]q over C for quivers of type ADET, together with the cup product, and more generally, the calculus structure. It turns out that the Hochschild cohomology also has a Batalin-Vilkovisky structure. I also computed the calculus structure for the centrally extended preprojective algebra,

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Eu, Ching-Hwa

Advisor dc:contributor.advisor

• Pavel Etingof.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45343

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45343