A Normal Form for Words in the Temperley-Lieb Algebra and the Artin Braid Group on Three Strands
Jack Hartsell · Digital Commons - East Tennessee State University (East Tennessee State University) · 2018
The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.