A semisimple Hopf algebra is a specific type of Hopf algebra that has a finite-dimensional representation theory and can be decomposed into simple components. This means it can be broken down into direct sums of simple algebras, which are similar to simple groups in group theory. Semisimple Hopf algebras play a crucial role in the study of representations, as they ensure that every finite-dimensional representation can be expressed as a direct sum of irreducible representations, making them easier to analyze and understand.
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