  A cohomology theory for multiplications and comultiplications of Frobenius
algebras is developed in low dimensions in analogy with Hochschild cohomology
of bialgebras based on deformation theory. Concrete computations are provided
for key examples.
  Skein theoretic constructions give rise to solutions to the Yang-Baxter
equation using multiplications and comultiplications of Frobenius algebras, and
2-cocycles are used to obtain deformations of R-matrices thus obtained.
