NDLI: Connection matrices and Lie algebra weight systems for multiloop chord diagrams

Content Provider	Springer Nature Link
Author	Schrijver, Alexander
Copyright Year	2015
Abstract	We give necessary and sufficient conditions for a weight system on multiloop chord diagrams to be obtainable from a metrized Lie algebra representation, in terms of a bound on the ranks of associated connection matrices. Here a multiloop chord diagram is a graph with directed and undirected edges so that at each vertex, precisely one directed edge is entering and precisely one directed edge is leaving, and each vertex is incident with precisely one undirected edge. Weight systems on multiloop chord diagrams yield the Vassiliev invariants for knots and links. The k-th connection matrix of a function f on the collection of multiloop chord diagrams is the matrix with rows and columns indexed by k-labeled chord tangles and with entries equal to the f value on the join of the tangles.
Ending Page	905
Page Count	13
Starting Page	893
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	4
Volume Number	42
Language	English
Publisher	Springer US
Publisher Date	2015-06-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Representations, algebraic theory (weights) Multiloop chord diagram Convex and Discrete Geometry Weight system Combinatorial aspects of groups and algebras Computer Science Invariants of knots and 3-manifolds Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Metrized Lie algebra Connection matrix Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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