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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

The stable Calabi-Yau dimension of the preprojective algebra of type $ {\mathbf L}_n$


Author: S. O. Ivanov
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 3.
Journal: St. Petersburg Math. J. 24 (2013), 475-484
MSC (2010): Primary 14J35
Published electronically: March 21, 2013
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Abstract: It is proved that if the characteristic of the ground field is not equal to $ 2$, then the stable Calabi-Yau dimension of the preprojective algebra of type $ {\mathbf L}_n$ is equal to $ 5$. This result contradicts certain claims by Erdmann and Skowroński related to the description of algebras whose stable Calabi-Yau dimension is $ 2$.


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Additional Information

S. O. Ivanov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Petrodvorets, St. Petersburg 198904, Russia
Email: sepa{\textunderscore}cmd@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01248-9
PII: S 1061-0022(2013)01248-9
Keywords: Preprojective algebras, self-injective algebras, Calabi--Yan dimension, stable category of modules
Received by editor(s): October 14, 2011
Published electronically: March 21, 2013
Additional Notes: Supported by RFBR (grant no. 10-01-00635); by targeted federal program “Scientific and Academic Specialists for Innovations in Russia” (grant nos. 2010-1.1-111-128-033, 14.740.11.0344); and by the St. Petersburg State University research program 6.38.74.2011 “Structure theory and geometry of algebraic groups and their applications in representation theory and algebraic K-theory”.
Article copyright: © Copyright 2013 American Mathematical Society