Abstract:We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional πΆ * -algebras π΅ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on πΏ 2 (π΅), the quantum adjacency matrices, or as certain operator bimodules over π΅ β² . We present a simple, purely algebraic approach to proving equivalence between these settings, thus recovering existing results in the tracial state setting. For non-tracial states, our approach naturally sugge… Show more
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