Bulg. J. Phys. vol.41 no.2 (2014), pp. 095-108



Physical Applications of Noncommutative Localization

P. Moylan
Physics Department, Pennsylvania State University, The Abington College, Abington, PA 19001 USA
Abstract. Construction of quotients, or localization as it is called in mathematics, provides a powerful tool to relate different physical structures which share some underlying similarities. For example, through localizations of enveloping algebras associated with the Poincaré group we can relate much of the representation theory of the Poincaré group to the representation theory of certain deformations of it, namely SO(2,3) and SO(1,4) [1,2]. Here we describe some additional physically interesting problems involving localization. We obtain results for the Lorentz and homogeneous Galilean groups similar to the just mentioned ones for the Poincaré group. We also describe some analogous results involving q deformations and supersymmetry, in particular, for Uq(sl(2)) and Uq(osp(1,2)). Our analysis leads to new representations of Uq(osp(1,2)).

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