Abstract
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebras have played an important role in mathematics and physics. This paper initiates the study of integral operators on lattices and the resulting Rota-Baxter lattices (of weight zero). We show that properties of lattices can be characterized in terms of their integral operators. We also display a large number of integral operators on any given lattice and classify the isomorphism classes of integral operators on some common classes of lattices. We further investigate structures on semirings derived from differential and integral operators on lattices.
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Acknowledgements
This work is supported by the NSFC Grants (Nos. 11801239 and 12171022). We thank the anonymous referees for their helpful suggestions.
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Gan, A., Guo, L. & Wang, S. Integral Operators on Lattices. Order 40, 63–86 (2023). https://doi.org/10.1007/s11083-021-09593-0
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DOI: https://doi.org/10.1007/s11083-021-09593-0