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arXiv · 2102.01553

Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor

Paolo Saracco
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Abstract

We prove how the universal enveloping algebra constructions for Lie-Rinehart algebras and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual motivation for the universal properties these constructions satisfy. As a supplement, the categorical approach offers new insights into the definitions of Lie-Rinehart algebra morphisms, of modules over Lie-Rinehart algebras and of the infinitesimal gauge algebra of a module.

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Paolo Saracco. 2021-02-02. Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor. https://doi.org/10.1007/s00009-022-01985-9

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