Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds

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dc.creatorAxenides, Minos
dc.creatorFloratos, Emmanuel
dc.date2008-09-20
dc.date2008-11-14
dc.date.accessioned2026-07-07T12:44:49Z
dc.date.available2026-07-07T12:44:49Z
dc.descriptionWe 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.
dc.description44 pages, v2:typos corrected, references added
dc.identifierhttps://arxiv.org/abs/0809.3493
dc.identifierhttp://arxiv.org/abs/0809.3493
dc.identifierJHEP 0902:039,2009
dc.identifierdoi:10.1088/1126-6708/2009/02/039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220901
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleNambu-Lie 3-Algebras on Fuzzy 3-Manifolds
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