An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models
Abstract
A dynamical fuzzy space might be described in terms of a dynamical three-index variable Cabc, which determines the algebraic relations fa fb =Cabc fc of the functions fa on a fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on fa. The solutions to the invariant equations of motion of Cabc can be generally constructed from the invariant tensors of Lie groups. Euclidean models the actions of which are bounded from below are introduced. Lie group symmetric solutions to a class of Euclidean model are obtained. The analysis of the fluctuations around the SO(3) symmetric solution shows that the solution can be regarded as a fuzzy S2/Z2.
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