  M-branes are related to theories on function spaces $\cal{A}$ involving
M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to
$\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms
of $T^M$ cannot be deformed when M>2, the arising M-algebras naturally relate
to Nambu's generalisation of Hamiltonian mechanics, e.g. by providing a
representation of the canonical M-commutation relations, $[J_1,\cdots,
J_M]=i\hbar$. Concerning multidimensional integrability, an important
generalisation of Lax-pairs is given.
