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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.

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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.

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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.
Funding AgencyGrant Number
Civilian Research & Development Foundation (CRDF)RM1-2545-MO-03
Subject Keywords:Preprojective algebra; Simple Lie algebra; Quiver
Issue or Number:1
Record Number:CaltechAUTHORS:20171004-092059005
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82036
Deposited By: Tony Diaz
Deposited On:04 Oct 2017 17:21
Last Modified:15 Nov 2021 19:47

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