NON-ABELIAN POISSON MANIFOLDS FROM D-BRANES
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Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is non-Abelian. Quantization further introduces noncommutativity as a deformation in powers of Planck's constant ℏ. Given an arbitrary simple Lie algebra [Formula: see text] and an arbitrary Poisson manifold ℳ, both finite-dimensional, we define a corresponding C⋆-algebra that can be regarded as a non-Abelian Poisson manifold. The latter provides a natural framework for a matrix-valued classical dynamics.
2007 ◽
Vol 17
(03)
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pp. 527-555
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1976 ◽
Vol 28
(2)
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pp. 420-428
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1985 ◽
Vol 37
(1)
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pp. 122-140
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2015 ◽
Vol 151
(7)
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pp. 1265-1287
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