Using an algebraic method previously introduced, we work out the mass spectra, symmetry breaking patterns, and topologies of general vacuum states in N=2 supersymmetric Chern-Simons-Higgs systems with adjoint matter coupling for arbitrary classical Lie groups. The approach is very general and only makes use of 'the property that the vacuum states satisfy the SU(2) algebra. Therefore, the results can also be applied to any systems that share the same property. In this kind of analysis, we obtain a natural basis for fields, which is useful for studying the self-dual solutions and quantum corrections in these systems.
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