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Dimensional-duality and Its Lie Groups

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Author(s): Nilotpal SINHA

Journal: Philosophic Nature
ISSN 0974-4215

Volume: 1;
Issue: 1;
Start page: 121;
Date: 2009;
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Keywords: Higher-Dimensional Geometry | Dimensional-Duality | Gravity | Lie Group

ABSTRACT
For a claim to a dimensional duality, we consider here that, the relativity is depending on a “double-fold” complexnumber for locally dense fourth axis within an enveloping 3D-space. This dimensional duality has been made herefor locally dense m-dimensional geometry within n-space, for m > n, if every axis of m-space is dimensional-dualto its enveloping n-space. This locally dense m-dimensional geometry describes a reflexive complex function, viz.,“transfusion” transformation, which establishes that, Lie group U(2) is the simply connected 1 to 2 enveloping groupof SO(3, 1) within D-dual spaces only. Again, using the weight vectors, it is found that, there exists a SU(4) group,which may be a symmetry group for gravitons.
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