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We show that even within the class of special biserial algebras, one of the most thoroughly studied classes of representation-tame finite dimensional algebras, the (left) big finitistic dimension may be strictly larger than the little. In fact, we find that the discrepancies Fin dim Λ – fin dim Λ fail to be bounded as Λ traces the special biserial algebras. More precisely: For every positive integer , we exhibit a special biserial algebra Λ with the property that fin dim Λ = +1, while Fin dim Λ=2+1.

Representation-Tame Algebras Need not be Homologically Tame