The representation type of the full transformation semigroup \(T_4\)
Let T-n 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 kT(n) is of finite representation type if n less than or equal to 3, According to Putcha, kT(n) is of infinite representation type if n greater than or equal to 5. Here, we deal with the remaining case n = 4 and show that kT(4) is also of finite representation type. Note that the quiver of kT(4) already has been exhibited by Putcha, here we determine the relations. It turns out that kT(4) is a string algebra and its global dimension is 3.
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429-434
429-434
Springer