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Register a new userCategorified Noncommutative manifolds
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Authors
R.A. Dawe Martins
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We construct a noncommutative geometry with generalised `tangent bundle from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class of real spectral triples where the Dirac operator is constructed from morphisms in a category. Applications for physics include quantisation via the tangent groupoid and new constraints on $D_{mathrm{finite}}$ (the fermion mass matrix).
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The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
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