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:

URL	URL Type	Description
https://doi.org/10.1016/j.jalgebra.2006.11.040	DOI	Article
http://www.sciencedirect.com/science/article/pii/S0021869307000385?via%3Dihub	Publisher	Article
https://arxiv.org/abs/math/0606403	arXiv	Discussion 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 Agency	Grant Number
NSF	DMS-0504847
Civilian Research & Development Foundation (CRDF)	RM1-2545-MO-03
NSF	DMS-0401387

Subject Keywords:

Preprojective algebra; Simple Lie algebra; Quiver

Issue or Number:

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)

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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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