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Hochschild homology and truncated cycles

Authors: Petter Andreas Bergh, Yang Han and Dag Madsen
Journal: Proc. Amer. Math. Soc. 140 (2012), 1133-1139
MSC (2010): Primary 16E40
Published electronically: November 23, 2011
MathSciNet review: 2869099
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Abstract: We study algebras having $2$-truncated cycles and show that these algebras have infinitely many nonzero Hochschild homology groups. Consequently, algebras of finite global dimension have no $2$-truncated cycles and therefore satisfy a higher version of the “no loops conjecture”.

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Additional Information

Petter Andreas Bergh
Affiliation: Institutt for Matematiske FAG, NTNU, N-7491 Trondheim, Norway
MR Author ID: 776982

Yang Han
Affiliation: KLMM, AMSS, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Dag Madsen
Affiliation: Department of Mathematics, 215 Carnegie, Syracuse University, Syracuse, New York 13244-1150
Address at time of publication: Profesjonshøgskolen, Universitetet i Nordland, 8049 Bodø, Norway
MR Author ID: 639380

Keywords: Hochschild homology, truncated cycles
Received by editor(s): July 12, 2010
Received by editor(s) in revised form: October 27, 2010, and November 26, 2010
Published electronically: November 23, 2011
Additional Notes: The first author was supported by NFR Storforsk grant No. 167130
The second author was supported by Project 10731070 NSFC
Dedicated: Dedicated to Professor Claus Michael Ringel on the occasion of his 65th birthday
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.