On M-Algebras, the Quantisation of Nambu-Mechanics, and Volume Preserving Diffeomorphisms
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 1996
- DOI:
- 10.48550/arXiv.hep-th/9602020
- arXiv:
- arXiv:hep-th/9602020
- Bibcode:
- 1996hep.th....2020H
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 16 pages, LaTex