On a Hopf Algebra in Graph Theory
On a Hopf Algebra in Graph Theory
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DOI：
10.1006/jctb.2000.1973
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发表时间：
2000-09
期刊：
影响因子：
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通讯作者：
S. Lando
中科院分区：
文献类型：
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作者：
S. Lando
我们介绍并开始研究的双代数的图，我们称之为4-双代数，和对偶双代数的4-不变量。4-双代数与W. T. Tutte在1946年，但它的结构更复杂。定义的根源是在低维拓扑，即在最近的理论Vassiliev结不变量。特别地，图的4-不变量决定了节点的Vassiliev不变量。这两个概念之间的关系进行了讨论。
We introduce and start the study of a bialgebra of graphs, which we call the 4-bialgebra, and of the dual bialgebra of 4-invariants. The 4-bialgebra is similar to the ring of graphs introduced by W. T. Tutte in 1946, but its structure is more complicated. The roots of the definition are in low dimensional topology, namely, in the recent theory of Vassiliev knot invariants. In particular, 4-invariants of graphs determine Vassiliev invariants of knots. The relation between the two notions is discussed.