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Vol. 1, No. 1 (2009) pp. 121-132

Abstract

Dimensional-duality and Its Lie Groups

NEIL SINHA

Excogitation & Innovation Laboratory, Atul Prasad Sarani, Hakimpara, Siliguri, W.B. 734006-05, India

Abstract: For a claim to a dimensional duality, we consider here that, the relativity is depending on a "double-fold" complex number for locally dense fourth axis within an enveloping 3D-space. This dimensional duality has been made here for locally dense m-dimensional geometry within n-space, for m > n, if every axis of m-space is dimensional-dual to 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 group of 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.