2026-09-18T21:43:43Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/453432022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Pavel Etingof.
Eu, Ching-Hwa
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2009-04-29T17:28:16Z
2009-04-29T17:28:16Z
2008
2008
http://hdl.handle.net/1721.1/45343
316795787
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
Includes bibliographical references (p. 227-229).
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,
by Ching-Hwa Eu.
Ph.D.
229 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Hochschild homology / cohomology of preprojective algebras of ADET quivers
Thesis
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