Type
Text
Type
Dissertation
Advisor
Kirillov, Alexander, Jr. | Sullivan, Dennis | Khovanov, Mikhail | Viro, Oleg.
Date
2012-08-01
Keywords
Algebra, Categorification, Homology, Quantum, Representation Theory, Topology | Theoretical mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71178
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Quantum sl2 gives rise to the Jones polynomial knot invariant. One of the insights of categorification is that this 3-dimensional picture is a shadow, the decategorification, of a 4-dimensional picture. Thus, the categorification of quantum sl2 gives rise through its representation theory to Khovanov homology, the categorification of the Jones polynomial. In the 3-dimensional picture, the algebra of Temperley-Lieb diagrams, used in the construction of the Jones polynomial, gives a graphical calculus for intertwiners of the representations of quantum sl2. We show that the algebra of Bar-Natan's dotted cobordisms, used in the construction of Khovanov homology, gives a graphical calculus for intertwiners of representations of categorified quantum sl2. | 54 pages
Recommended Citation
Chatav, Eitan, "Representation Theory of Categorified Quantum sl2" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 385.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/385