Published May 15, 2006
| Submitted
Journal Article
Open
Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups
- Creators
- Etingof, Pavel
- Rains, Eric
Abstract
Preprojective algebras of quivers were introduced in 1979 by Gelfand and Ponomarev [GP], because for quivers of finite ADE type, they are models for indecomposable representations (they contain each indecomposable exactly once). Twenty years later, these algebras and their deformed versions introduced in [CBH] (for arbitrary quivers) became a subject of intense interest, since their representation varieties, called quiver varieties, played an important role in geometric representation theory. Ironically, it is exactly for quivers of finite ADE type that preprojective algebras fail to have good properties—they are not Koszul and their deformed versions are not flat.
Additional Information
© 2006 Elsevier Inc. Received 21 March 2005, Available online 24 January 2006. The work of the author was partially supported by the NSF Grant DMS-9988796 and the CRDF Grant RM1-2545-MO-03. The author was supported in part by NSF Grant No. DMS-0401387. P.E. is grateful to W. Crawley-Boevey for the references [Ru,CB2], and to M. Artin, J. de Jong, V. Ostrik, D. Rogalski, and R. Rouquier for useful discussions.Attached Files
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Additional details
- Eprint ID
- 81972
- DOI
- 10.1016/j.jalgebra.2006.01.005
- Resolver ID
- CaltechAUTHORS:20171002-152707569
- DMS-9988796
- NSF
- RM1-2545-MO-03
- Civilian Research & Development Foundation (CRDF)
- DMS-0401387
- NSF
- Created
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2017-10-02Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field