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We study representations of MV-algebras -- equivalently, unitallattice-ordered abelian groups -- through the lens of Stone-Priestley duality,using canonical extensions as an essential tool. Specifically, the theory ofcanonical extensions implies that the (Stone-Priestley) dual spaces ofMV-algebras carry the structure of topological partial commutative orderedsemigroups. We use this structure to obtain two different decompositions ofsuch spaces, one indexed over the prime MV-spectrum, the other over the maximalMV-spectrum. These decompositions yield sheaf representations of MV-algebras,using a new and purely duality-theoretic result that relates certain sheafrepresentations of distributive lattices to decompositions of their dualspaces. Importantly, the proofs of the MV-algebraic representation theoremsthat we obtain in this way are distinguished from the existing work on thistopic by the following features: (1) we use only basic algebraic facts aboutMV-algebras; (2) we show that the two aforementioned sheaf representations arespecial cases of a common result, with potential for generalizations; and (3)we show that these results are strongly related to the structure of theStone-Priestley duals of MV-algebras. In addition, using our analysis of thesedecompositions, we prove that MV-algebras with isomorphic underlying latticeshave homeomorphic maximal MV-spectra. This result is an MV-algebraicgeneralization of a classical theorem by Kaplansky stating that two compactHausdorff spaces are homeomorphic if, and only if, the lattices of continuous[0, 1]-valued functions on the spaces are isomorphic.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality