Integral Operators on Lattices

Aiping Gan, Li Guo, Shoufeng Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
JournalOrder
DOIs
StateAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

Keywords

  • Dendriform semiring
  • Derivation
  • Differential lattice
  • Integral operator
  • Lattice
  • Novikov semiring
  • Rota-Baxter lattice
  • Semiring

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