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The article examines finite dimensional Hopf algebras that are quotients of the upper-triangular subalgebra of the quantum groups that were introduced by V. G. Drinfel'd and M. Jimbo. It offers information on finite dimensional algebras which are either tame, finite, or wild representation types. It adds that the algebraic structures give rise to solutions of the Yang-Baxter equation by the universal R-matrix that is acting on it and the modular category of representations.