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An invariant approach to dynamical fuzzy spaces with a three-index variable

Naoki Sasakura
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Abstract

A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. 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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Naoki Sasakura. 2005-06-29. An invariant approach to dynamical fuzzy spaces with a three-index variable. https://doi.org/10.1142/s0217732306020329

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