Lie algebraic noncommuting structures from reparametrization symmetry

We extend our earlier work of revealing both space-space and space-timenoncommuting structures in various models in particle mechanics exhibitingreparametrisation symmetry. We show explicitly (in contrast to the earlierresults in our paper \cite{sg}) that for some special choices of thereparametrisation parameter $\epsilon$, one can obtain space-space noncommutingstructures which are Lie-algebraic in form even in the case of the relativisticfree particle. The connection of these structures with the existing models inthe literature is also briefly discussed. Further, there exists some values of$\epsilon$ for which the noncommutativity in the space-space sector can be madeto vanish. As a matter of internal consistency of our approach, we also studythe angular momentum algebra in details.Comment: 9 pages Latex, some references adde