All Questions

Let $G$ be a finite group and $k$ a field of characteristic $p$ dividing $|G|$. A perfect complex of $kG$-modules is by definition a finite complex of finitely generated projective ($=$ injective $=$ ...

Let $A$ be a selfinjective algebra and for an indecomposable module $M$ define $\psi_M:= \inf \{ i \geq 1 | Ext_A^i(M,M) \neq 0 \}$. Questions: In case $A$ is symmetric, do we have $\psi_M \leq max \...

Recently I have been considering a problem that has had me venture into some mathematical territory that is new to me, specifically group representations, words, and character theory. I would ...

Let $G$ be a finite group. By a $G$-lattice I mean a finitely generated free abelian group $L$ with an action of $G$. One says that $L$ is a permutation lattice if $L$ has a $\mathbb{Z}$-basis ...

If $A$ is an algebra over a field $k$ and $M$ is a finite-dimensional $A$-module, then Alperin showed in a paper [Diagrams for modules, JPAA, 1980] how to associate a diagram to $M$ with the vertices ...

Let $G$ be a finite group and $\phi:M\to N$ be a surjective homomorphism of $G$-lattices (i.e. finitely generated $\mathbb{Z}[G]$-modules, free as $\mathbb Z$-modules), with kernel $K$. For every $n\...