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Published July 1, 2007 | Submitted
Journal Article Open

On central extensions of preprojective algebras

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.

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.

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Created:
August 22, 2023
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March 5, 2024