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.Comment: 18 pages; Based on Review Talk at the Workshop on "Noncommutative
Field Theory and Gravity", Corfu Summer Institute on Elementary Particles and
Physics, September 8-12, 2010, Corfu, Greece; to be published in Proceedings
of Scienc
