ON FROBENIUS ALGEBRAS AND THE QUANTUM YANG-BAXTER EQUATION

It is shown that every Frobenius algebra over a commutative ring deter mines a class of solutions of the quantum Yang-Baxter equation, which forms a subbimodule of its tensor square. Moreover, this subbimodule i s free of rank one as a left (right) submodule. An explicit form of a generator is given in terms of the Frobenius homomorphism. It turns ou t that the generator is invertible in the tensor square if and only if the algebra is Azumaya.