An invariant approach to dynamical fuzzy spaces with a three-index variable
Abstract
A dynamical fuzzy space might be described by a three-index variable Cabc, which determines the algebraic relations fa fb =Cabc fc among the functions fa on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on fa. I study equations for the three-index variable invariant under the general linear transformation, and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, I study SO(3) symmetric solutions, and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.
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