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Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor (2102.01553v1)
Published 2 Feb 2021 in math.RA and math.CT
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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