4
$\begingroup$

I had seen an exercise:

Write the Loewy-diagram of the direct indecomposable modules of the $A = K\Gamma / I$ algebra, where \begin{align*} \Gamma: 1 \underset{\beta}{\overset{\alpha}{\rightleftarrows}} 2 \underset{\delta}{\overset{\gamma}{\rightleftarrows}} 3, \quad I = (\alpha \beta, \beta \alpha - \gamma \delta, \delta \gamma). \end{align*}

Unfortunately I couldn't find the definition, or a way to compute, of Loewy-diagram.

Could someone point me to a resource explaining it?

$\endgroup$
1
  • $\begingroup$ This is actually a good question. You see the term Loewy-diagram often but I am also not aware of a formal definition in the literature. It probably just means the decomposition of the Loewy factors $J^iM/J^{i+1}M$ into simple moduels of a module $M$. $\endgroup$ – Mare Oct 29 '19 at 12:09
0
$\begingroup$

A somewhat formal definition of the Loewy structure (which is the same as how Mare described, and I'm sure this is the Loewy-diagram you're looking for) can be found in Benson's treatise in Lecture Notes in Mathematics. See Appendix, page 174.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.