Oriented Quantum Algebras and Invariants of Knots and Links

Abstract

In our previous work oriented quantum algebras were motivated and introduced in a very natural categorical setting within the context of knots and links, some examples were discussed, and a rudimentary theory of oriented quantum algebras was sketched. Invariants of knots and links can be computed from oriented quantum algebras. Here we continue the study of oriented quantum algebras. We view them from a more algebraic perspective and develop a more detailed theory for them and their associated invariants. We study a class of examples associated with the HOMFLY polynomial in depth.