All Questions

Let $k$ be a field, $G$ a finite group, and $k[G]$ the group algebra. Let $A$ be a subalgebra of $k[G]$. In general, $A$ is not the group algebra of some subgroup $H$ of $G$. Question: Is there any ...

Let $G$ be a finite group. Let $p$ be a prime number such that $p \mid |G|$. Let Irr$(G)$ denote the set of ordinary irreducible characters of $G$. For $\chi\in$ Irr$(G)$ define $e_{\chi} := \frac{\...

Let $\Gamma$ be a finitely generated group and let $A=\mathbb{C}[\Gamma]$ be the corresponding group algebra over $\mathbb{C}$. Let $X$ be the set of all maximal left ideals of $A$ and let $X_0=\{I \...

Let $K$ be a large enough finite field, let $A$ be a finite-dimensional $K$-algebra. Moreover, let $M$ be a finitely generated $A$-module and let $M = M_1\oplus ... \oplus M_n$ be a decomposition of $...

Can you characterize the unit-group of the real group-algebra of the extraspecial plus-type 2-group of order 128? (That is $\mathbb{R}[2_+^{1+6}]$ using Conway's notation.) (Please choose any irrep ...