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Communications in Algebra Volume 39, 2011 - Issue 12
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Original Articles

Calabi–Yau Coalgebras

J.-W. He Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing Zhejiang, China; Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium
,
B. Torrecillas Department of Algebra and Analysis, University of Almeria, Almeria, Spain
,
F. Van Oystaeyen Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium
&
Y. Zhang Department WNI, University of Hasselt, Hasselt, BelgiumCorrespondence[email protected]
Pages 4644-4661 | Received 07 Sep 2010, Published online: 14 Dec 2011
 
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Abstract

We present a method for constructing the minimal injective resolution of a simple comodule of a path coalgebra of quivers with relations. Dual to the Calabi–Yau condition of algebras, we introduce the concept of a Calabi–Yau coalgebra, and then describe the Calabi–Yau coalgebras of low global dimensions.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENT

The authors thank the referee for his/her careful reading of the manuscript and the valuable comments and suggestions. The work is supported by an FWO-grant and NSFC (No. 10801099) and STDZ (No. 2011R10051). The first named author wishes to thank the Department of Algebra and Analysis of the University of Almeria for its hospitality during his visit.

Notes

Communicated by S. Montgomery.

Dedicated to our friend Mia Cohen.

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