  The standard formulation of Jacobi manifolds in terms of differential
operators on line bundles, although effective at capturing most of the relevant
geometric features, lacks a clear algebraic interpretation similar to how
Poisson algebras are understood to be the algebraic counterpart of Poisson
manifolds. We propose a formalism, based on the dimensioned algebra technology
recently developed by the author, to capture the algebraic counterparts of
Jacobi manifolds as dimensioned Poisson algebras. Particularly, we give a
generalisation of the functor $\text{C}^\infty:\textsf{Smooth}\to
\textsf{Ring}$ for line bundles and Jacobi manifolds, we show that coisotropic
reduction of Jacobi manifolds provides an example of algebraic reduction of
dimensioned Poisson algebras and we discuss the relation between products of
Jacobi manifolds and the tensor products of their associated dimensioned
Poisson algebras. These results motivate the definition of the category of
poly-line bundles, defined as collections of line bundles over the same base
manifold, and the corresponding generalisation of Jacobi structures into this
context, the so-called poly-Jacobi manifolds. We present some preliminary
results about these generalisations and discuss potential future lines of
research. An interesting outcome of this research is a somewhat surprising
connection between geometric mechanics and dimensional analysis. This is
suggested by the fact that if one assumes a phase space to be a poly-Jacobi
manifold, the observables -- which are the dimensioned analogue of real-valued
functions -- carry a natural partial addition and total multiplication
structure identical to the usual algebra of physical quantities in dimensional
analysis.
