霍普夫代数、分配（Laplace）对和Hash积：群特征标张量积分解的统一方法
Hopf Algebras, Distributive (Laplace) Pairings and Hash Products: A unified approach to tensor product decompositions of group characters
摘要：
证明了双交换分次连通霍普夫代数的2-上链卷积幺半群的某个分配（Laplace）子群参数化了某些表现良好的霍普夫代数变形.使用拉普拉斯群或其Frobenius子群，我们定义了更高导出的散列积，并发展了一个一般理论来研究它们的主要性质。将我们的结果应用于对称函数的双交换分次连通霍普夫代数，证明了经典的张量积和特征分解，如一般线性群，混合协变和反变或有理特征，正交和辛群特征，Thibon和约化对称群特征，都是高导hash积的特例.在附录中，我们讨论了与形式群律的关系。
英文摘要：
We show for bicommutative graded connected Hopf algebras that a certain distributive (Laplace) subgroup of the convolution monoid of 2-cochains parameterizes certain well behaved Hopf algebra deformations. Using the Laplace group, or its Frobenius subgroup, we define higher derived hash products, and develop a general theory to study their main properties. Applying our results to the (universal) bicommutative graded connected Hopf algebra of symmetric functions, we show that classical tensor product and character decompositions, such as those for the general linear group, mixed co- and contravariant or rational characters, orthogonal and symplectic group characters, Thibon and reduced symmetric group characters, are special cases of higher derived hash products. In the Appendix we discuss a relation to formal group laws.
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