In this paper we study the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decomposition can be explicitly expressed in terms of characters and the Haar integral. In this paper we investigate Hopf algebras with the Chevalley property, which are not necessarily semisimple. We find explicit expressions for idempotents in terms of Hopf-algebraic data, where the Haar integral is replaced by the regular character of the dual Hopf algebra. For a large class of Hopf algebras, these are shown to form a complete set of orthogonal idempotents. We give an example which illustrates that the Chevalley property is crucial.

在本文中，我们研究了特征为零的代数闭合域上有限维Hopf代数的正则模的同型分解。对于半简单的Hopf代数，可以用字符和Haar积分明确表示实现同型分解的等幂。在本文中，我们研究具有Chevalley属性的Hopf代数，它们不一定是半简单的。我们用Hopf代数数据找到了幂等的显式表达式，其中Haar积分被对偶Hopf代数的正则字符代替。对于一大类Hopf代数，它们被显示为形成完整的正交幂等集。我们举一个例子说明Chevalley属性至关重要。