The Brauer group of Sweedler's Hopf algebra H-4

We calculate the Brauer group of the four dimensional Hopf algebra H-4 intr oduced by M. E. Sweedler. This Brauer group BM(k; H-4, R-0) is defined with respect to a (quasi-) triangular structure on H-4, given by an element R-0 is an element of H-4 x H-4. In this paper k is a field. The additive group (k, +) of k is embedded in the Brauer group and it fits in the exact and s plit sequence of groups: 1 --> (k, +) --> BM(k, H-4, R-0) --> BW(k) --> 1 where BW(k) is the well-known Brauer-Wall group of k. The techniques involv ed are close to the Clifford algebra theory for quaternion or generalized q uaternion algebras.