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The Grothendieck Algebra Of A Hopf Algebra, I   
摘  要:   Introduction We began in [4] a study of the Grothendieck group G(H) of the category of finite dimensional right comodules of a Hopf algebra H. We begin here the study of the representation theory of the algebras G(H) K obtained from G(H) by extending the scalars. Our primary motivation has been to try to establish Kaplansky's conjecture that if a finite dimensional cosemisimple Hopf algebra H over an algebraically closed field contains a simple subcoalgebra of dimension n 2 , then n divides the dimension of H. As a more direct attack on the problem has not been successful, we have been studying the problem from a general point of view. Our question can be viewed as a conjecture about a character of G(H), so we have been developing information about the represe

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