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On central extensions of preprojective algebras

Etingof, Pavel and Latour, Frédéric and Rains, Eric (2007) On central extensions of preprojective algebras. Journal of Algebra, 313 (1). pp. 165-175. ISSN 0021-8693. doi:10.1016/j.jalgebra.2006.11.040. https://resolver.caltech.edu/CaltechAUTHORS:20171004-092059005

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Abstract

We show that the Hilbert polynomial P(t) of the trace space A/[A,A] of the centrally extended preprojective algebra A of an ADE quiver is equal to the Hilbert series of the maximal nilpotent subalgebra of the corresponding simple Lie algebra under the principal gradation. This implies that the Hilbert polynomial of the center of A is t^(2h−4)P(1/t), where h is the Coxeter number.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jalgebra.2006.11.040DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021869307000385?via%3DihubPublisherArticle
https://arxiv.org/abs/math/0606403arXivDiscussion Paper
Additional Information:© 2007 Elsevier Inc. Received 16 June 2006, Available online 24 January 2007. P.E. thanks George Lusztig for a useful discussion. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. F.L. thanks the IHÉS in Bures-sur-Yvette, France. E.R. was supported in part by NSF grant DMS-0401387.
Funders:
Funding AgencyGrant Number
NSFDMS-0504847
Civilian Research & Development Foundation (CRDF)RM1-2545-MO-03
NSFDMS-0401387
Subject Keywords:Preprojective algebra; Simple Lie algebra; Quiver
Issue or Number:1
DOI:10.1016/j.jalgebra.2006.11.040
Record Number:CaltechAUTHORS:20171004-092059005
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171004-092059005
Official Citation:Pavel Etingof, Frédéric Latour, Eric Rains, On central extensions of preprojective algebras, Journal of Algebra, Volume 313, Issue 1, 1 July 2007, Pages 165-175, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2006.11.040. (http://www.sciencedirect.com/science/article/pii/S0021869307000385)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82036
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Oct 2017 17:21
Last Modified:15 Nov 2021 19:47

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