Calabi-Yau coalgebras
J.-W. He, B. Torrecillas, F. Van Oystaeyen, Y. Zhang
TL;DR
This paper introduces the Calabi-Yau condition for coalgebras, constructs minimal injective resolutions for simple comodules of path coalgebras, and describes Calabi-Yau coalgebras with low global dimensions.
Contribution
It extends the Calabi-Yau concept to coalgebras and provides new descriptions and properties of Calabi-Yau coalgebras with low global dimensions.
Findings
Calabi-Yau coalgebras characterized by lower global dimensions.
Construction of minimal injective resolutions for simple comodules.
Properties of cohom functors related to Calabi-Yau coalgebras.
Abstract
We provide a construction of minimal injective resolutions of simple comodules of path coalgebras of quivers with relations. Dual to Calabi-Yau condition of algebras, we introduce the Calabi-Yau condition to coalgebras. Then we give some descriptions of Calabi-Yau coalgebras with lower global dimensions. An appendix is included for listing some properties of cohom functors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology