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- W1586982023 abstract "The rank-three tensor models, which have a rank-three tensor as their only dynamical variable, may be interpreted as models of dynamical fuzzy spaces. In this interpretation, the generalized Hermiticity condition on the rank-three tensor leads to a cyclic property of the algebra of functions on fuzzy spaces. The fuzzy spaces with the cyclic property are shown to have various physically interesting characteristics. (i) Although the function algebras of the kind are nonassociative in general, various properties analogous to quantum mechanics hold on the fuzzy spaces. (ii) The symmetry of the rank-three tensor models can be shown to be represented systematically by n-ary transformations on the fuzzy spaces. The transformations contain, for instance, diffeomorphism on fuzzy spaces. (iii) There exists a systematic procedure of truncating the function algebras of the kind, and it can be used to consider subspaces, compactifications, lattice theories, and coarsegraining procedures of fuzzy spaces in physical applications." @default.
- W1586982023 created "2016-06-24" @default.
- W1586982023 creator A5034359780 @default.
- W1586982023 date "2012-03-28" @default.
- W1586982023 modified "2023-10-17" @default.
- W1586982023 title "Fuzzy spaces from tensor models, cyclicity condition, and n-ary algebras" @default.
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- W1586982023 doi "https://doi.org/10.48550/arxiv.1203.6170" @default.
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