### Nambu-Lie 3-Algebras on Fuzzy 3-ManifoldsNambu-Lie 3-Algebras on Fuzzy 3-Manifolds

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 Author Axenides, Minos ♦ Floratos, Emmanuel Source arXiv.org Content type Text File Format PDF Date of Submission 2008-09-20 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ Mathematical Physics ♦ Mathematics - Quantum Algebra ♦ math ♦ physics:hep-th ♦ physics:math-ph Abstract We consider Nambu-Poisson 3-algebras on three dimensional manifolds ${\cal M}_{3}$, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms $SDiff({\cal M}_{3})$ is identical to the Nambu-Poisson algebra on ${\cal M}_{3}$. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation of $SDiff({\cal M}_{3})$. We propose a quantization prescription for the Nambu-Poisson algebra which provides us with the correct classical limit. As such it possesses all of the expected classical properties constituting, in effect, a concrete representation of Nambu-Lie 3-algebras. Description Reference: JHEP 0902:039,2009 Educational Use Research Learning Resource Type Article Page Count 44