Braid group representations via the Yang Baxter equation
by Franko, Jennifer M., Ph.D., INDIANA UNIVERSITY, 2007, 62 pages; 3278226

Abstract:

One of the major goals of this thesis is to determine the images of the braid group under representations afforded by the Yang Baxter equation when the solution is a non trivial 4 × 4 matrix. Making the assumption that all the eigenvalues of the Yang Baxter solution are roots of unity leads to the conclusion that all the images are finite. More precisely, given the above assumptions we have the following short exact sequence: 1→ImPn →ImBn→ Sn→1 and Im(Bn) is finite.

Using results of Turaev, we have also identified cases in which one would get a link invariant. Finally, by observing the group algebra generated by the image of the braid group sometimes factor through known algebras, in certain instances we can identify the invariant.

 
AdvisersZhenghan Wang; Kent Orr
SchoolINDIANA UNIVERSITY
SourceDAI/B 68-09, p. , Dec 2007
Source TypeDissertation
SubjectsMathematics
Publication Number3278226
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