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Condition of indecomposability in the definition of wild representation type

In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms. Usually I've seen the de …
Jacob FG's user avatar
  • 497
6 votes
1 answer
445 views

Tame-Wild dichotomy; why can't tame algebras be wild?

I would like to understand the Tame-Wild dichotomy, and in particular why an algebra cannot be tame and (semi-)wild at the same time. I've looked in the papers by Drozd and Crawley-Boevey [D80, CB88]. …
Jacob FG's user avatar
  • 497
3 votes
1 answer
185 views

Explicit proof that algebra is derived wild

Following the terminology of Drozd, Yuriy A., Derived tame and derived wild algebras, Algebra Discrete Math. 2004, No. 1, 57-74 (2004). ZBL1067.16028. let $A$ and $R$ be algebras over a field $k$. A s …
Jacob FG's user avatar
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1 vote
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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, J. Algebra 322, No. 7, 2433-2448 (2009). ZBL1191.16017.
Jacob FG's user avatar
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