Hochschild homology / cohomology of preprojective algebras of ADET quivers
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2009
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| Online Access: | http://hdl.handle.net/1721.1/45343 |
| _version_ | 1826210745856032768 |
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| author | Eu, Ching-Hwa |
| author2 | Pavel Etingof. |
| author_facet | Pavel Etingof. Eu, Ching-Hwa |
| author_sort | Eu, Ching-Hwa |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. |
| first_indexed | 2024-09-23T14:55:02Z |
| format | Thesis |
| id | mit-1721.1/45343 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:55:02Z |
| publishDate | 2009 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/453432019-04-12T09:56:49Z Hochschild homology / cohomology of preprojective algebras of ADET quivers Eu, Ching-Hwa Pavel Etingof. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2009-04-29T17:28:16Z 2009-04-29T17:28:16Z 2008 2008 Thesis http://hdl.handle.net/1721.1/45343 316795787 eng 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. http://dspace.mit.edu/handle/1721.1/7582 229 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Eu, Ching-Hwa Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title | Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title_full | Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title_fullStr | Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title_full_unstemmed | Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title_short | Hochschild homology / cohomology of preprojective algebras of ADET quivers |
| title_sort | hochschild homology cohomology of preprojective algebras of adet quivers |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/45343 |
| work_keys_str_mv | AT euchinghwa hochschildhomologycohomologyofpreprojectivealgebrasofadetquivers |