This notion was introduced by Doi and Takeuchi last year.
[See, Contemporary Mathematics 267, 2000, pp67-97.]
They are both Frobenius algebras and Frobenius coalgebras
and satisfy some compatibility conditions. They generalize
finite dimensional Hopf algebras. Many results (e.g. Radford
S^4 formula) can be generalized to biFrobenius algebras.
In my talk I am going to explain some basic properties and
to give some new results.