INCIDENCE HOPF-ALGEBRAS
INCIDENCE HOPF-ALGEBRAS
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DOI：
10.1016/0022-4049(94)90105-8
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发表时间：
1994-10-21
影响因子：
0.8
通讯作者：
SCHMITT, WR
中科院分区：
文献类型：
--
作者：
SCHMITT, WR
我们给出了关于偏序集族的关联Hopf代数的几个结果，包括它们的代数结构的刻画，在余交换情况下寻找本原元生成集的一种组合方法，以及对包括FAA di Bruno Hopf代数在内的一类代数成立的对极的行列式公式。我们介绍了来自图族、拟阵和分配格的各种关联Hopf代数的例子，其中许多例子推广了著名的Hopf代数。
We present several results about incidence Hopf algebras of families of partially ordered sets, including a characterization of their algebra structure, a combinatorial technique for finding generating sets of primitive elements in the cocommutative case, and a determinant formula for the antipode which holds for a class including the Faa di Bruno Hopf algebra. We introduce a variety of examples of incidence Hopf algebras arising from families of graphs, matroids and distributive lattices, many of which generalize well-known Hopf algebras.