The well-known tame theorem tells that for a given tame bocs and a positive integer n there exist finitely many minimal bocses, such that any representation of the original bocs of dimension at most n is isomorphic to the image of a representation of some minimal bocses under a certain reduction functor. In the present paper we will give an alternative statement of the tame theorem in terms of matrix problem, by constructing a unified minimal matrix problem whose indecomposable matrices cover all the canonical forms of the indecomposable representations of dimension at most n for each non-negative integer n.
Let A = kQ/I be a finite-dimensional Nakayama algebra, where Q is an Euclidean diagram An for some n with cyclic orientation, and I is an admissible ideal generated by a single monomial relation. In this note we determine explicitly all the Hochschild homology and cohomology groups of A based on a detailed description of the Bardzell complex. Moreover, the cyclic homology of A can be calculated in the case that the underlying field is of characteristic zero.
