
TL;DR
This paper explores the structure of Lie-Rinehart algebras within the Loday-Pirashvili tensor category and establishes a functorial relationship to Leibniz algebroids, advancing the understanding of algebraic structures in this context.
Contribution
It introduces a novel perspective on Lie-Rinehart algebras in the Loday-Pirashvili category and constructs a functor to Leibniz algebroids, linking these algebraic frameworks.
Findings
Defined Lie-Rinehart algebras in the Loday-Pirashvili category
Constructed a functor from these algebras to Leibniz algebroids
Provided new insights into algebraic structures in tensor categories
Abstract
We describe Lie-Rinehart algebras in the tensor category of linear maps in the sense of Loday and Pirashvili and construct a functor from Lie-Rinehart algebras in to Leibniz algebroids.
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