# Reduction algorithm for non-(semi-)free bocses

A bocs (also box) is a pair $(A,V)$, where $A$ is a $k$-algebra (or a (skeletally) small $k$-category) and $V$ is an $A$-coalgebra.

The category of representations of bocses is given by

• objects: representations of $A$
• morphisms $\operatorname{Hom}_{bocs}(M,N):=\operatorname{Hom}_A(V\otimes_A M, N)$.

Special kinds of boxes (so called free, or semi-free boxes) were used by Drozd [Drozd: Tame and wild matrix problems] in his famous proof of the tame-wild dichotomy for algebras. (see also [Crawley-Boevey: On tame algebras and bocses]) The essential step method is the so-called reduction algorithm which gives you a method to change the box "a little bit" such that its representation theory doesn't change "too much".

The preprint [Bekkert, Drozd: Tame-wild dichotomy for derived categories] suggests that such an algorithm also works for certain non-(semi-)free boxes, although the proofs do not contain many details.

I'm looking for other references dealing with a reduction algorithm for certain non-semi-free boxes.

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