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Let $A$ be a unital algebra, defined over the complex numbers. Any bimodule $M$ over $A$ must, by definition, be a left, and right, module satisfing $$ a.(m.b) = (a.m).b, ~~~~~~~ \textrm{ for all } a, …

Given two semisimple unital algebras $A$ and $B$, defined over $\mathbb{R}$ or $\mathbb{C}$, denote their categories of representations by $_A\mathcal{M}$ and $_B\mathcal{M}$ respectively. Can one des …

Given a fundamental representation $V(\nu_k)$ of a semisimple Lie algebra $\frak{g}$, and a general irreducible finite-dimensional representation $V$, is it ever possible that the tensor product $V \o …

For the $D_n$-series simple Lie algebra $\frak{so}_{2n}$ a curious phenomenon occurs for the fundamental representations corresponding to the spinor nodes of the Dynkin diagram, which is to say the sp …

Let $A$ be a noncommutative algebra over a field, say $\mathbb{C}$ or $\mathbb{R}$, and let $L$ be a bimodule over $A$. If $L$ is invertible, that is, if the dual right $A$-module $L^*$ satisfies $$ L …