The Temperley-Lieb Algebra and the Artin Braid Group
摘要
The Temperley-Lieb algebra was originally described in the work of two physicists; Temperley and Lieb. However, this algebra has deep connections to knot theory and 3-manifold invariants. For example, its connection to knot theory stems from Louis H. Kauffman’sKauffman, L. H. interpretation of the Temperley-Lieb algebra as a diagrammatic algebra consisting of n-tanglestangle as its basis. In this lecture we explore the basics of the Temperley-Lieb algebra and Artin braid group.