On Non Commutative G2 structure

Details On Non Commutative G2 structure On Non Commutative G2 structure

2004-08-02

arxiv.org/abs/hep-th/0408011v2

J.Phys. A38 (2005) 2773-2784

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, Latex. Typos corrected, minor changes. Version to appear in J. Phys.A: Math.Gen.(2005)

Scientific paper

10.1088/0305-4470/38/12/017

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras. We show that there are eight possible solutions for this extended structure, one of which corresponds to the commutative case. Then we obtain a matrix representation solving such algebras using combinatorial arguments. An application to matrix model of M-theory is discussed.

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