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Let $A$ be a complex associative and unital algebra. Denote by $A\text{-mod}$ the category of finite-dimensional left modules over $A$. This is an Abelian category and we denote by $\text{Ch}_{\ge 0} (...

Suppose $0\to A \stackrel{\iota}{\to} B \stackrel{\pi}{\to} C \to 0$ is a short exact sequence of groups. We have an induced map $k[\iota] : k[A] \to k[B]$ of group algebras over a field $k$. What ...