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Lie Group Mathematics: " The Math of String Theory " Helen Hegener I also include a fullMathematical Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological groups. Lie groups represent the best developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. Lie groups provide a natural framework for