Hochschild homology / cohomology of preprojective algebras of ADET quivers
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316795787-MIT.pdf
Description
Full printable version
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6.7 MB
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Adobe PDF
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7dbe7698d7f54a1c8bdea316cc4078cc
Author(s)
Eu, Ching-Hwa
Advisor(s)
Pavel Etingof.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
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,
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
Includes bibliographical references (p. 227-229).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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