JP Journal of Geometry and Topology
Volume 8, Issue 1, Pages 23 - 39
(March 2008)
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DIRICHLET BRANES AND A COHOMOLOGICAL DEFINITION OF TIME FLOW
José M. Isidro (Spain) and P. Fernández De Córdoba (Spain)
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Abstract:
Dirichlet branes are objects whose transverse
coordinates in space are matrix-valued functions. This leads to considering a
matrix algebra or, more generally, a Lie algebra, as the classical phase space
of a certain dynamics where the multiplication of coordinates, being given by
matrix multiplication, is nonabelian. Further quantising this dynamics by means
of a é-product introduces
noncommutativity (besides non- abelianity) as a quantum ¤-deformation. The algebra of functions on a standard
Poisson manifold is replaced with the universal enveloping algebra of the given
Lie algebra. We define generalised Poisson brackets on this universal enveloping
algebra, examine their properties, and conclude that they provide a natural
framework for dynamical setups (such as coincident Dirichlet branes) where
coordinates are matrix-valued, rather than number-valued, functions. |
| Keywords and phrases: Dirichlet branes, Lie algebra, cohomology. |
| Communicated by Yasuo Matsushita |
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