Following the terminology of


*Drozd, Yuriy A.*, [**Derived tame and derived wild algebras**](https://doi.org/10.48550/arXiv.math/0310171), Algebra Discrete Math. 2004, No. 1, 57-74 (2004). [ZBL1067.16028](https://zbmath.org/1067.16028).


let $A$ and $R$ be algebras over a field $k$. A strict family of $A$-complexes based on $R$ is a complex $P^\* \in K^-(A\otimes R^{\rm{op}})$ of finitely generated projective $A-R$-bimodules such that


* For every indecomposable finite dimensional $R$-module $L$, $P^\*\otimes\_R L$ is indecomposable.
* For every pair of finite dimensional $R$-modules $L$ and $L'$, if $P^\* \otimes L \cong P^\*\otimes L'$ then $L \cong L'$.


An algebra $A$ is called derived wild if there exists a strict family for every finite dimensional algebra $R$.


My question is: Does anyone have an explicit description of such a strict family for a (preferably simple) derived wild algebra $A$ and some wild algebra $R$, say $R = k\langle x,y \rangle$ for example.



Explicit proof that algebra is derived wild
A few such examples are constructed in


*Bekkert, Viktor; Drozd, Yuriy; Futorny, Vyacheslav*, [**Derived tame local and two-point algebras**](https://doi.org/10.1016/j.jalgebra.2009.05.023), J. Algebra 322, No. 7, 2433-2448 (2009). [ZBL1191.16017](https://zbmath.org/1191.16017).


