| Abstract: | Let Tn be the semigroup of all transformations of a set of n elements and k a field of characteristic 0. According to Ponizovskii, the semigroup algebra kTn is of finite representation type if n h 3. According to Putcha, kTn is of infinite representation type if n S 5. Here, we deal with the remaining case n=4 and show that kT4 is also of finite representation type. Note that the quiver of kT4 already has been exhibited by Putcha, here we determine the relations. It turns out that kT4 is a string algebra and its global dimension is 3. |
