University of Sydney
School of Mathematics and Statistics
Chalmers University & University of Gothenburg,
Frobenius approach to Hopf algebras
Friday 7th August, 12-1pm, Carslaw 273.
Let A be a Frobenius algebra over a commutative ring R.
It turns out that Frobenius structure on A defines canonically
a solution of the Yang-Baxter equation.
Using the fact that finite projective
Hopf algebras over rings with trivial Picard group are Frobenius,
we obtain an explicit formula for this solution in terms of the
integral and antipode. We use this formula to prove that
the antipode S in finite projective Hopf algebras has a finite order.
Further, we prove that if the algebra has a constant rank N, as a
projective module, then S4N=id.