We propose generalized quantization axioms for Nambu-Poisson manifolds, which allow for a geometric interpretation of n-Lie algebras and their enveloping algebras. We illustrate these axioms by describing extensions of Berezin-Toeplitz quantization to produce various examples of quantum spaces of relevance to the dynamics of M-branes, such as fuzzy spheres in diverse dimensions. We briefly describe preliminary steps towards making the notion of quantized 2-plectic manifolds rigorous by extending the groupoid approach to quantization of symplectic manifolds.
|Number of pages||18|
|Journal||Proceedings of Science|
|Publication status||Published - 31 Jan 2011|
|Event||Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity - Corfu, Greece|
Duration: 8 Sep 2010 → 12 Sep 2010