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The reflection equations (RE) are a consistent extension of the Yang-Baxterequations (YBE) with an addition of one element, the so-called reflectionmatrix or $K$-matrix. For example, they describe the conditions forfactorizable scattering on a half line just like the YBE give the conditionsfor factorizable scattering on an entire line. The YBE were generalized todefine quadratic algebras, \lq Yang-Baxter algebras\rq\ (YBA), which were usedintensively for the discussion of quantum groups. Similarly, the RE definequadratic algebras, \lq the reflection equation algebras\rq\ (REA), which enjoyvarious remarkable properties both new and inherited from the YBA. Here wefocus on the various properties of the REA, in particular, the quantum groupcomodule properties, generation of a series of new solutions by composing knownsolutions, the extended REA and the central elements, etc.Comment: 31 pages, 8 figures (not included

Covariance Properties of Reflection Equation Algebras